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STAT MISC / MATH 1410 / MATH1410 / SOPHIA STATISTICS UNIT 1 – MILESTONE 1, UNIT 2 – MILESTONE 2, UNIT 3 – MILESTONE 3, UNIT 4 – MILESTONE 4, UNIT 5 MILESTONE 5 AND FINAL MILESTONE
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MATH 1410 / MATH1410 STATISTICS UNIT 1 – MILESTONE 1
MATH 1410 / MATH1410 STATISTICS UNIT 1 – MILESTONE 1 You passed this Milestone Jenae noticed that many of her co-workers would op... [Show More] t for the coffee that appeared to be most recently brewed, regardless of the flavor of the coffee offered. This leads her to believe that what she was witnessing was not really representative of everyone's true flavor preferences. She adapted her experimental study accordingly. Select one control in Jenae's experimental study. Jenae places condiments at random places throughout the kitchen. Jenae makes sure that the coffee in different pots is brewed at the same time. Jenae uses different locations in the kitchen for the coffee pots. Jenae monitors the habits of the co-workers who do not drink coffee. RATIONALE In an experiment, controls are when conditions are manipulated by the experimenter to keep conditions as consistent as possible. In this example Jenae brews coffee at the same time, so this is a control. CONCEPT Experimental Design I need help with this question 2 The traffic volumes at a major intersection in New York were surveyed every day between one and four in the afternoon for a month to study the traffic patterns in the city. Which of the following types of bias affects the conclusions of the survey? Selection bias Deliberate bias Response bias Non-response bias RATIONALE Selection bias is when the mode of selection introduces a bias in the sample so that it is not representative of the population of interest. Since they only collected information from 1 to 4pm, this is a selection bias. CONCEPT Selection and Deliberate Bias I need help with this question 3 A new pet food product for small dogs has been developed to help with tooth decay. Fifty-two dogs participate in the study. Each dog owner picks a card from a standard deck out of a hat. If the card is red, their dog will be in the treatment group. If the card is black, their dog will be in the placebo group. Which experimental design was used? Case-Control Design Randomized Block Design Matched-Pair Design Completely Randomized Design RATIONALE Since all dogs are assigned treatment or control randomly by picking a card without considering other factors, this is called a completely randomized design. CONCEPT Completely Randomized Design I need help with this question 4 Sam counts how many people came to the local political meeting. He counts 72 people, but forgot about the 4 people sitting behind him. The percent error in his calculation is . -5.3% 50% -2.8% 5.6% RATIONALE Recall that the percent error is equivalent to the absolute difference divided by the actual value. If the actual number of people was 76, and the observed number of people was only 72, then the absolute error is: So we calculate the percentage error to be: CONCEPT Absolute Change and Relative Change I need help with this question 5 In a study to assess the risk of obesity with the amount of time exercised per week, researchers matched each patient, in a sample of 500 people who are obese, with a person of the same ethnicity, gender, and age (along with other similar characteristics) who is not obese. The researchers asked the patients and their matches a series of questions, and then tracked eating and exercise habits regularly for several years. Which type of statistical study are the researchers conducting? Prospective study Retrospective study Case-control study Designed experiment RATIONALE Since the study collected information on people over several years moving forward, it is a prospective study design. CONCEPT Prospective and Retrospective Studies I need help with this question 6 A shoe retailer decides to record the styles and sizes of shoes that his customers choose. He records this data for an entire year by keeping track of his customers' purchases. Which statement accurately describes the type of data the shoe retailer is collecting? The shoe retailer is gathering raw data because he is recording shoe sizes and styles by himself. The shoe retailer is receiving raw data on shoe sizes and styles from nearby shoe companies. The shoe retailer is gathering available data because customers tell him which shoe sizes and styles they prefer. The shoe retailer is receiving available data on shoe sizes and styles from nearby shoe companies. RATIONALE Since the retailer is gathering the data himself, this would be an example of raw data. CONCEPT Data I need help with this question 7 The manager of an amusement park conducts a survey among the people visiting the park to learn their favorite rides. Out of 100 people randomly selected to complete the survey, 25 people have chosen not to participate. The manager's survey suffers from which of the following types of bias? There is no bias in the way this survey is carried out. Nonresponse bias Selection bias Response bias RATIONALE Since 75% of the people didn't respond to the survey, we would worry about nonresponse bias, which means those who didn't respond would produce a very different outcome than those who did respond. CONCEPT Nonresponse and Response Bias I need help with this question 8 An insurance firm wants to estimate the percentage of senior citizens in a small town with approximately 2,534 residents. It asks a group of 85 randomly selected people in the town about their age. Select the statement that is TRUE. The sample is 85 people. The population is 2,534 people. None of the answer choices are true. The sample is 2,534 people. The population is 85 people. The sample is 85 people. The population is 2,449 people. RATIONALE Recall the entire set of interest is the population and a sample is a subset of that population. In this question the entire set is the 2534 residents, with the sample being the 85 that were chosen to be analyzed about their age. CONCEPT Sampling I need help with this question 9 Which of the following data types will be continuous? The number of children younger than ten that visited a planetarium last week The letter grades students received on a class quiz The number of cars in 100 households The total weight of apples harvested in the farm in a season RATIONALE The total weight of apples can take on any value and is therefore continuous. The other measures can only take on a limited number of values and are discrete. CONCEPT Discrete vs. Continuous Data I need help with this question 10 A study in which results are measured without intervention from the researcher is called a(n) . Pilot study Observational study Controlled experiment Simple random sample RATIONALE Recall that an observational study is one in which there is no control over the setting in any way. CONCEPT Observational Studies and Experiments I need help with this question 11 Choose the statement that accurately describes how a city government could apply systematic random sampling. Every resident is divided into groups, and 1,000 people are randomly selected to participate in a survey about city services. Every fifth person in a population is selected to participate in a survey about city services. Every resident in five neighborhoods is selected to participate in a survey about city services. Every individual over the age of 18 is selected to participate in a survey about city services. RATIONALE A systematic sample is when every nth element is chosen from the population. In this case, by choosing every 5th household, this makes is a systematic sample. CONCEPT Simple Random and Systematic Random Sampling I need help with this question 12 A pizza owner asked 50 customers to taste a new type of topping and found that 40 people liked its taste. Which of these is an example of descriptive statistics? 80% of all people like the taste of the pizza topping. 80% of the surveyed customers like the taste of the pizza topping. 80% of the people in the city where the pizza shop is located like the taste of the pizza topping. 80% of all the pizza shop's customers like the taste of the pizza topping. [Show Less]
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MATH 1410 / MATH1410 STATISTICS UNIT 2 – MILESTONE 2
MATH 1410 / MATH1410 STATISTICS UNIT 2 – MILESTONE 2 You passed this Milestone The manager went over the sales of mobile phones a... [Show More] t the store and found that the mean sale was 45, with a standard deviation of 4. On a particular day, 52 mobile phones were sold. What is the z-score of the sale of mobile phones on that day? -28 28 1.75 -1.75 RATIONALE Recall that the z-score can be calculated with the following formula: The given value is 52 phones, the mean is 45 phones, and the standard deviation is 4 phones. Plug these values in to get the following z-score: This also tells us that 52 is 1.75 z-scores or standard deviations above the mean. CONCEPT Standard Scores and Z-Scores I need help with this question 2 In a poll of 300 preschoolers, 125 said they preferred chocolate ice cream, 71 said they preferred vanilla, 100 said they preferred cookies & cream, and 4 said they had never eaten ice cream. If a pie chart were to be made showing the preference for each flavor, the central angle for the chocolate ice cream sector would be . 41° 5° 150° 124° RATIONALE Recall that to get the angle for something in a pie chart we use the following formula: open parentheses fraction numerator v a l u e over denominator t o t a l space v a l u e end fraction close parentheses times 360 degree So in this case, the central angle for the chocolate ice cream sector would be: CONCEPT Bar Graphs and Pie Charts I need help with this question 3 The first quartile (Q1) value from the above box plot is . 47 40 65 54 RATIONALE Note the value for Q1 is the left edge of the box, which is 47. CONCEPT Five Number Summary and Boxplots I need help with this question 4 Select the statement that accurately describes unimodal distribution. A distribution in which two distinct values are more frequent than the other values. A distribution in which the values are distributed uniformly. A distribution in which one value is more frequent than other values. A distribution in which numerous values are more frequent than other values. RATIONALE Recall the mode is the most frequently occurring value. If a distribution is unimodal, it simply means there is one value that occurs most frequently. CONCEPT Shapes of Distribution I need help with this question 5 Choose the statement that correctly describes a normal distribution. Approximately 68% of the values are greater than the mean value. The approximate percent of values lying within three standard deviations of the mean is 49.85%. Approximately 68% of the values lie within one standard deviation of the mean. The approximate percent of values lying within two standard deviations of the mean is 47.5%. RATIONALE The normal distribution follows the empirical rule. This tells us that within one standard deviation of the mean, we should find roughly 68% of the data. CONCEPT Normal Distribution I need help with this question 6 Sara wonders what percentage of her students answered at least half of the quiz questions incorrectly. The relative cumulative frequency of students who earned a score of 20 or lower on the quiz is . 68% 28% 34% 14% RATIONALE To get the relative frequency of 20 or lower, we need to find the cumulative number of 20 or less. We simply add up any bin that has the number 20 or less, such as the bin that shows scores of 1-5, 6-10, 11-15, and 16-20. This would be: To get relative frequency, we will take this cumulative number and divide it by the total number of students. CONCEPT Cumulative Frequency I need help with this question 7 Dave drives to work. While driving the car over nine days, he observes his daily average speed and lists it in the table below. Day Average Speed (MPH) 1 45 2 62 3 44 4 70 5 59 6 66 7 54 8 63 9 67 The median speed at which Dave drove to work was . 62 miles per hour 58.89 miles per hour 59 miles per hour 63 miles per hour RATIONALE To get the median we first order the data and take the middle value. The ordered values are: Since there are an odd number (n=9) of values we simply take the middle, which is 62 mph. CONCEPT Mean, Median, and Mode I need help with this question 8 Which of the following statements is true? For a large enough sample size, the Central Limit Theorem states that the sample medians of repeated samples of a population are normally distributed. For the Central Limit Theorem to be true, you must have a large sample, the underlying population must be normally distributed, and the standard deviation should not be finite. Even with a very large sample size, the Central Limit Theorem states that the sample means of repeated samples of a population cannot be normally distributed. For a large enough sample size, the Central Limit Theorem states that the sample means of repeated samples of a population are normally distributed. RATIONALE The Central Limit Theorem gives us information about the properties' sampling distributions of statistics to have given that the sample size is large enough. It tells us the sampling distribution's mean should be equal to the true population mean. CONCEPT Shape of a Sampling Distribution I need help with this question 9 The weekly salaries of full-time and part-time employees at a company are listed on the table. What does the circled section represent? Sixty-eight full-time employees earn $34 per week. Two full-time employees earn more than $680 per week. Thirty-four part-time employees earn more than $680 per week. Two part-time employees earn between $680 and $690 per week. RATIONALE If we recall that the stem and leaf can give us the actual values in the data set, then the circle corresponds to $683 and $684. We can then note that there are two part-time workers who make between $680 and $690. CONCEPT Stem-and-Leaf Plots I need help with this question 10 In a survey to rate the customer service department of a company, 300 persons rated their agreement with the statement, "The staff is helpful and courteous." The information was put into a table. Rating Frequency Strongly Agree 32 Agree 50 Neutral 97 Disagree 53 Strongly Disagree 68 The relative frequency of people who strongly disagree with the statement is . 22.7% 10.7% 40.3% 68% [Show Less]
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MATH 1410 / MATH1410 STATISTICS UNIT 3 – MILESTONE 3
MATH 1410 / MATH1410 STATISTICS UNIT 3 – MILESTONE 3 You passed this Milestone Which of the following is a property of binomial d... [Show More] istributions? The sum of the probabilities of successes and failures is always 1. All trials are dependent. The expected value is equal to the number of successes in the experiment. There are exactly three possible outcomes for each trial. RATIONALE Recall that for any probability distribution, the sum of all the probabilities must sum to 1. CONCEPT Binomial Distribution I need help with this question 2 Zhi and her friends moved on to the card tables at the casino. Zhi wanted to figure out the probability of drawing a face card or an Ace. Choose the correct probability of drawing a face card or an Ace. Answer choices are in the form of a percentage, rounded to the nearest whole number. 8% 4% 31% 25% RATIONALE Since the two events, drawing a face card and drawing an ace card, are non-overlapping, we can use the following formula: CONCEPT "Either/Or" Probability for Non-Overlapping Events I need help with this question 3 John is playing a game with a standard deck of playing cards. He wants to draw a jack on the first try. Which of the following statements is true? The probability that John draws a jack on the first try is 1/13. If John replaces the card, re-shuffles, and draws again, the probability that he will pull another jack increases. The probability that John draws a jack on the first try is 1/13. If John replaces the card, re-shuffles, and draws again, the probability that he will pull another jack stays the same. The probability that John draws a jack on the first try is 3/13. If John replaces the card, re-shuffles, and draws again, the probability that he will pull another jack stays the same. The probability that John draws a jack on the first try is 1/13. If John replaces the card, re-shuffles, and draws again, the probability that he will pull another jack decreases. RATIONALE Events are said to be independent if one event does not influence the likelihood of the other. Since John re- shuffles the deck and puts the card back in the deck, the probability should be the same and the first draw will not influence the second. CONCEPT Independent vs. Dependent Events I need help with this question 4 A magician asks an audience member to pick any number from 6 to 15. What is the theoretical probability that an individual chooses the number the magician has in mind? RATIONALE If we suppose that the card chosen by the magician is fixed, then there are 10 possible values, {6, 7, 8, 9, 10, 11, 12, 13, 14, or 15}, that are all equally likely. So, the probability that a specific value is chosen is: CONCEPT Theoretical Probability/A Priori Method I need help with this question 5 Select the following statement that describes non-overlapping events. Receiving the Queen of Diamonds fulfills Luke's need of getting both a face card and a diamond. Luke wants a red card so he can have a winning hand, and he receives the five of clubs. Luke needs to roll an odd number to win. When it’s his turn, he rolls a five. To win, Luke needs a black card. He receives an eight of spades. RATIONALE Events are non-overlapping if the two events cannot both occur in a single trial of a chance experiment. Since he wants a red card {Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, or King: In either Diamond or Hearts} and he got the Five of Clubs, there is no overlap. CONCEPT Overlapping Events I need help with this question 6 Jake tosses a coin and rolls a six-sided die. All of the following are possible outcomes EXCEPT: Tails, Three Heads, Seven Heads, Five Tails, One RATIONALE Recall a coin has heads and tails and a standard die has six values, {1, 2, 3, 4, 5, or 6}. So, obtaining a value of 7 is not possible. CONCEPT Outcomes and Events I need help with this question 7 Asmita went to a blackjack table at the casino. At the table, the dealer has just shuffled a standard deck of 52 cards. Asmita has had good luck at blackjack in the past, and she actually got three blackjacks with Aces in a row the last time she played. Because of this lucky run, Asmita thinks that Ace is the luckiest card. The dealer deals the first card to her. In a split second, she can see that it is a non-face card, but she is unsure if it is an Ace. What is the probability of the card being an Ace, given that it is a non-face card? Answer choices are in a percentage format, rounded to the nearest whole number. 8% 77% 69% 10% RATIONALE The probability of it being an Ace given it is a Non-face card uses the conditional formula: Note, that in a standard deck of 52 cards, there are 12 face cards, so 40 non-face cards. Of those non-face cards, there are only 4 Aces. CONCEPT Conditional Probability I need help with this question 8 Patricia was having fun playing poker. She needed the next two cards dealt to be spades so she could make a flush (five cards of the same suit). There are 12 cards left in the deck, and three are spades. What is the probability that the two cards dealt to Patricia (without replacement) will both be spades? Answer choices are in percentage format, rounded to the nearest whole number. 17% 18% 5% 25% RATIONALE If there are 12 cards left in the deck with 3 spades, the probability of being dealt 2 spades if they are dealt without replacement means that we have dependent events because the outcome of the first card will affect the probability of the second card. We can use the following formula: The probability that the first card is a spade would be 3 out of 12, or . The probability that the second card is a spade, given that the first card was also a spade, would be because we now have only 11 cards remaining and only two of those cards are spades (since the first card was a spade). So we can use these probabilities to find the probability that the two cards will both be spades: CONCEPT "And" Probability for Dependent Events I need help with this question 9 David is playing a game where he flips two coins and counts the total number of heads. The possible outcomes and probabilities are shown in the probability distribution below. What is the expected value for the number of heads from flipping two coins? 1 2 3 1.5 RATIONALE The expected value, also called the mean of a probability distribution, is found by adding the products of each individual outcome and its probability. We can use the following formula to calculate the expected value, E(X): CONCEPT Expected Value I need help with this question 10 Using the Venn Diagram below, what is the conditional probability of event A occurring, assuming that event B has already occurred [P(A|B)]? 0.05 0.22 0.71 0.10 RATIONALE To get the probability of A given B has occurred, we can use the following conditional formula: The probability of A and B is the intersection, or overlap, of the Venn diagram, which is 0.1. The probability of B is all of Circle B, or 0.1 + 0.35 = 0.45. CONCEPT Conditional Probability I need help with this question 11 The average number of tunnel construction projects that take place at any one time in a certain state is 3. Find the probability of exactly five tunnel construction projects taking place in this state. 0.048 0.023 0.10 0.020 [Show Less]
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MATH 1410 / MATH1410 STATISTICS UNIT 4 – MILESTONE 4
MATH 1410 / MATH1410 STATISTICS UNIT 4 – MILESTONE 4 You passed this Milestone The table below shows the grade and reading level ... [Show More] for 5 students. Grade Reading Level Student 1 2 6 Student 2 6 14 Student 3 5 12 Student 4 4 10 Student 5 1 4 For grade, the mean is 3.6 and the standard deviation is 2.1. For reading level, the mean is 9.2 and the standard deviation is 4.1. Using the formula below or Excel, find the correlation coefficient, r, for this set of students. Answer choices are rounded to the nearest hundredth. 1.00 0.85 0.71 0.92 RATIONALE In order to get the correlation, we can use the formula: Correlation can be quickly calculated by using Excel. Enter the values and use the function "=CORREL(". CONCEPT Correlation I need help with this question 2 This scatterplot shows the maintenance expense for a truck based on its years of service. The equation for least regression line to this data set is ŷ = 76.82x + 88.56. What is the predicted value (in dollars) for maintenance expenses when a truck is 7 years old? $549 $473 $626 $703 RATIONALE In order to get the predicted maintenance expense when the age of the truck is 7 years, we simply substitute the value 7 in our equation for x. So we can note that: CONCEPT Predictions from Best-Fit Lines I need help with this question 3 Raoul lives in Minneapolis and he is planning his spring break trip. He creates the scatterplot below to assess how much his trip will cost. Which answer choice correctly indicates the explanatory and response variables for the scatterplot? Explanatory variable: Distance Response variable: Cost Explanatory variable: Minneapolis Response variable: Miles flown Explanatory variable: Miles flown Response variable: Minneapolis Explanatory variable: Cost Response variable: Distance RATIONALE The explanatory variable is what is along the horizontal axis, which is distance. The response variable is along the vertical axis, which is cost. CONCEPT Explanatory and Response Variables I need help with this question 4 Which of the following scatterplots shows a correlation affected by an influential point? RATIONALE An influential point will influence correlation that doesn't lie in the range of the other data. This graphs shows an outlier that is above the other data and lower in the x-direction. CONCEPT Cautions about Correlation I need help with this question 5 Peter analyzed a set of data with explanatory and response variables x and y. He concluded the mean and standard deviation for x as 7.8 and 3.70, respectively. He also concluded the mean and standard deviation for y as 12.2 and 4.15, respectively. The correlation was found to be 0.964. Select the correct slope and y-intercept for the least-squares line. Answer choices are rounded to the hundredths place. Slope = -1.08 y-intercept = 3.78 Slope = 1.08 y-intercept = -3.78 Slope = 1.08 y-intercept = 3.78 Slope = -1.08 y-intercept = -3.78 RATIONALE We first want to get the slope. We can use the formula: To then get the intercept, we can solve for the y-intercept by using the following formula: y with hat on top equals b subscript 0 plus b subscript 1 x We know the slope, b subscript 1, and we can use the mean of x and the mean of y for the variables x and y with hat on top to solve for the y-intercept, b subscript 0. CONCEPT Finding the Least-Squares Line I need help with this question 6 In a study of 30 high school students, researchers found a high correlation, 0.93, between amount of exercise and weight lost. Which of the following statements is TRUE? There is a strong positive linear association between weight loss and exercise, but the researchers have not proven causation. The researchers proved that exercise causes weight loss, but only for high school students. The researchers proved that exercise causes weight loss. 93% of the high school students studied lost weight. RATIONALE Recall that correlation measures the strength and direction of linear association. So r= 0.93 indicates a strong positive linear association. Recall also, that correlation doesn't imply causation. Causation is a direct change in one variable causing a change in some outcome. CONCEPT Correlation and Causation I need help with this question 7 For the data plotted in the scatterplot, the r2 value was calculated to be 0.9846. Which of the following sets of statements is true? 98.5% of the variation in age is explained by a linear relationship with yearly income. The correlation coefficient, r, is 0.969. 98.5% of the variation in yearly income is explained by a nonlinear relationship with age. The correlation coefficient, r, is 0.992. 98.5% of the variation in yearly income is explained by a linear relationship with age. The correlation coefficient, r, is 0.992 98.5% of the variation in age is explained by a nonlinear relationship with yearly income. The correlation coefficient, r, is 0.969. RATIONALE The coefficient of determination measures the percent of variation in the outcome, y, explained by the regression. So a value of 0.9846 tells us the regression with age, x, can explain about 98.5% of the variation in income, y. We can also note that r = . CONCEPT Coefficient of Determination/r^2 I need help with this question 8 A correlation coefficient between average temperature and coat sales is most likely to be . between 1 and 2 between 0 and 1 between 0 and -1 between -1 and -2 RATIONALE If we note that as temp goes up, we would expect coats to be less necessary, so coat sales would go down. So correlation should be negative and this would be between 0 and -1. CONCEPT Positive and Negative Correlations I need help with this question 9 Thomas was interested in learning more about the salary of a teacher. He believed as a teacher increases in age, the annual earnings also increases. The age (in years) is plotted against the earnings (in dollars) as shown below. Using the best-fit line, approximately how much money would a 45-year-old teacher make? $50,000 $58,000 $48,000 $55,000 RATIONALE To get a rough estimate of the salary of a 45 year-old, we go to the value of 45 on the horizontal axis and then see where it falls on the best-fit line. This looks to be about $50,000. CONCEPT Best-Fit Line and Regression Line I need help with this question 10 Jesse takes two data points from the weight and feed cost data set to calculate a slope, or average rate of change. A hamster weighs half a pound and costs $2 per week to feed, while a Labrador Retriever weighs 62.5 pounds and costs $10 per week to feed. Using weight as the explanatory variable, what is the slope of a line between these two points? Answer choices are rounded to the nearest hundredth. $7.75 / lb. $4.00 / lb. $6.25 / lb. $0.13 / lb. RATIONALE In order to get slope, we can use the formula: s l o p e equals fraction numerator y 2 minus y 1 over denominator x 2 minus x 1 end fraction. Using the information provided, the two points are: (0.5 lb., $2) and (62.5 lb., $10). We can note that: CONCEPT Linear Equation Algebra Review I need help with this question 11 Brad reads a scatterplot that displays the relationship between the number of cars owned per household and the average number of citizens who have health insurance in neighborhoods across the country. The plot shows a strong positive correlation. Brad recalls that correlation does not imply causation. In this example, Brad sees that increasing the number of cars per household would not cause members of his community to purchase health insurance. Identify the lurking variable that is causing an increase in both the number of cars owned and the average number of citizens with health insurance. Average annual salary per household The number of different car brands The number of citizens in the United States who do not have health insurance Average health insurance costs in the United States RATIONALE Recall that a lurking variable is something that must be related to the outcome and explanatory variable that when considered can help explain a relationship between 2 variables. Since higher income is positively related to owning more cars and having health insurance, this variable would help explain why we see this association. CONCEPT Correlation and Causation I need help with this question 12 Shawna finds a study of American women that had an equation to predict weight (in pounds) from height (in inches): ŷ = -260 + 6.6x. Shawna’s height was 64 inches and her weight was 150 pounds. What is the value of the residual for Shawna's weight and height? -12.4 pounds 730 pounds 12.4 pounds 162.4 pounds RATIONALE Recall that to get the residual, we take the actual value - predicted value. So if the actual height of 64 inches and the resulting actual weight is 150 pounds, we simply need the predicted weight. Using the regression line, we can say: The predicted weight is 164.4 pounds. So the residual is: CONCEPT Residuals I need help with this question 13 Which of the following scatterplots shows an outlier in the y-direction? RATIONALE To have an outlier in the y-direction the outlier must be in the range of x data but outside the range of y-data. This outlier is outside of the data in the y direction, lying below all of the data. CONCEPT Outliers and Influential Points I need help with this question 14 Which of the following is a guideline for establishing causality? The experiment performed should be controlled and randomized. Do not consider other possible causes. Look for cases where correlation does not exist between the variables. Check if the effect is present or absent when the response variable is present or absent. [Show Less]
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MATH 1410 / MATH1410 STATISTICS UNIT 5 – MILESTONE 5
MATH 1410 / MATH1410 STATISTICS UNIT 5 – MILESTONE 5 You passed this Milestone Which of the following is an example of a paramete... [Show More] r? Half of the receipts at the coffee shop include web address for giving feedback. 9047 out of 531,310 citizens voted in the special election for city council. 3.5% of the restaurant goers are given a survey to fill out. All of the members of the community watch group gave their availability to volunteer over the summer. RATIONALE Recall a parameter comes from the entire set of interest, the population. Since they are looking at all members of a community here, their availability to volunteer would be an example of a parameter. CONCEPT Sample Statistics and Population Parameters I need help with this question 2 A school is gathering some data on its sports teams because it was believed that the distribution of boys and girls were evenly distributed across all the sports. This table lists the number of boys and girls participating in each sport. Boys Girls Tennis 18 30 Soccer 42 15 Swimming 12 18 Select the observed and expected frequencies for the boys participating in soccer. Observed: 42 Expected: 22.5 Observed: 42 Expected: 24 Observed: 57 Expected: 24 Observed: 57 Expected: 22.5 RATIONALE If we simply go to the chart then we can directly see the observed frequency for boys participating in soccer is 42. To find the expected frequency, we need to find the number of occurrences if the null hypothesis is true, which in this case, was that the three options are equally likely, or if the three options were all evenly distributed. First, add up all the options in the boys column: If each of these three options were evenly distributed among the 72 boys, we would need to divide the total evenly between the three options: This means we would expect 24 boys to choose tennis, 24 boys to choose soccer, and 24 boys to choose swimming. CONCEPT Chi-Square Statistic I need help with this question 3 Sukie interviewed 125 employees at her company and discovered that 21 of them planned to take an extended vacation next year. What is the 95% confidence interval for this population proportion? Answer choices are rounded to the hundredths place. 0.11 to 0.21 0.10 to 0.23 0.16 to 0.17 0.11 to 0.16 RATIONALE In order to get the CI we want to use the following form. p with hat on top plus-or-minus z to the power of asterisk times square root of fraction numerator p with hat on top q with hat on top over denominator n end fraction end root First, we must determine the corresponding z*score for 95% Confidence Interval. Remember, this means that we have 5% for the tails, meaning 5%, or 0.025, for each tail. Using a z-table, we can find the upper z-score by finding (1 - 0.025) or 0.975 in the table. This corresponding z-score is at 1.96. We can know p with hat on top comma space q with hat on top comma space a n d space n. So putting it all together: The lower bound is: 0.168-0.065 =0.103 or 0.10 The upper bound is: 0.168+0.065 =0.233 or 0.23 CONCEPT Confidence Interval for Population Proportion I need help with this question 4 Select the statement that correctly describes a Type II error. A Type II error occurs when the null hypothesis is accepted when it is actually false. A Type II error occurs when the null hypothesis is rejected when it is actually true. A Type II error occurs when the null hypothesis is accepted when it is actually true. A Type II error occurs when the null hypothesis is rejected when it is actually false. RATIONALE Recall a Type II error is when we incorrectly accept a false null hypothesis. In this case, we want to reject and conclude there is evidence is correct. CONCEPT Type I/II Errors I need help with this question 5 Henri has calculated a z-test statistic of -2.73. What is the p-value of the test statistic? Answer choices are rounded to the thousandths place. 0.004 0.006 0.003 0.394 RATIONALE If we go to the chart and the row for the z-column for -2.7 and then the column 0.03, this value corresponds to 0.0032 or 0.003. CONCEPT How to Find a P-Value from a Z-Test Statistic I need help with this question 6 One condition for performing a hypothesis test is that the observations are independent. Marta is going to take a sample from a population of 600 students. How many students will Marta have to sample without replacement to treat the observations as independent? 540 60 120 300 RATIONALE In general we want about 10% or less to still assume independence. So size = 0.1*N = 0.1(600) = 60 A sample of 60 or less would be sufficient. CONCEPT Sampling With or Without Replacement I need help with this question 7 Brad recorded the number of visitors at the local science museum during the week: Day Visitors Tuesday 18 Wednesday 24 Thursday 28 Friday 30 He expected to see 25 visitors each day. To answer whether the number of visitors follows a uniform distribution, a chi-square test for goodness of fit should be performed. (alpha = 0.10) What is the chi-squared test statistic? Answers are rounded to the nearest hundredth. 2.54 1.40 3.36 1.12 RATIONALE Using the chi-square formula we can note the test statistic is CONCEPT Chi-Square Test for Goodness-of-Fit I need help with this question 8 What value of z* should be used to construct a 97% confidence interval of a population mean? Answer choices are rounded to the thousandths place. 2.17 1.65 1.88 1.96 [Show Less]
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MATH 1410 / MATH1410 STATISTICS FINAL MILESTONE
MATH 1410 / MATH1410 STATISTICS FINAL MILESTONE You passed this Milestone This chart shows the number of students of different age ... [Show More] groups who participated in a quiz. Which of the following statements about the stack plot is true? There were more male students in the age group 19-21 than in the age group 15-17. There were more male students than female students in the age group 19-21. There were more female students in the age group 17-19 than in any other age group. There were more students in the age group 15-17 than in any other age group. RATIONALE If we note that the greatest area for the girls is the longest darker region, this occurs in the age group 17-19. CONCEPT Stack Plots I need help with this question 2 Jay wants to study nutrition and performance in schools using available data. Which of the scenarios below will provide Jay with available data? Going to a local high school and asking the principal for information about students' previous grades, then interviewing a random selection of students about their eating habits. Going to a local high school and asking the principal for information about students' current and previous grades, then interviewing a random selection of students about their eating habits. Going to a local high school and asking the principal for information about students' current and previous grades, then asking the health teacher for the results from a survey students took in health class. Going to a local college and asking current undergraduates to report their grades and eating habits from high school. RATIONALE Recall, for data to be considered available data it must already be collected. Since the grades data and survey data were already collected these are examples of available data. CONCEPT Data I need help with this question 3 Regan wants to study how reading on a computer affects comprehension among elementary school students. Regan thinks that girls and boys might differ and he also suspects that grade level will affect the results. He decides to create a male and a female group for each grade. Within each group, he randomly assigns half of the students to read an article on paper and half of the students to read the article on a computer. Which type of experimental design does this situation illustrate? Completely Randomized Randomized Block Double-Blind Matched-Pair RATIONALE Since students are put into gender and grade blocks and are then assigned treatment or control randomly this is called a randomized block design. CONCEPT Randomized Block Design I need help with this question 4 Select the correct statement regarding experiments. A researcher can control the environment and observe the response. A researcher cannot control the environment but can observe the response. A researcher can control the environment but cannot observe the response. A researcher can neither control the environment nor observe the response. RATIONALE The defining part of experimental setting is that the researcher can control the setting and apply some treatment to observe how it affects an outcome of interest. CONCEPT Observational Studies and Experiments I need help with this question 5 Rachel measured the lengths of a random sample of 100 screws. The mean length was 2.9 inches, and the population standard deviation is 0.1 inch. To see if the batch of screws has a significantly different mean length from 3 inches, what would the value of the z-test statistic be? 1 10 -10 -1 RATIONALE If we first note the denominator of Then, getting the z-score we can note it is This tells us that 2.9 is 10 standard deviations below the value of 3, which is extremely far away. CONCEPT Z-Test for Population Means I need help with this question 6 Jesse takes two data points from the weight and feed cost data set to calculate a slope, or average rate of change. A ferret weighs 2.1 pounds and costs $3.40 per week to feed, while a Labrador Retriever weighs 70 pounds and costs $7.50 per week to feed. Using weight as the explanatory variable, what is the slope of the line between these two points? Answer choices are rounded to the nearest hundredth. $1.62 / lb. $1.73 / lb. $16.56 / lb. $.06 / lb. RATIONALE In order to get slope, we can use the formula: s l o p e equals fraction numerator y 2 minus y 1 over denominator x 2 minus x 1 end fraction. Using the information provided, the two points are: (2.1 lb., $3.40) and (70 lb., $7.50). We can note that: CONCEPT Linear Equation Algebra Review I need help with this question 7 Eric is randomly drawing cards from a deck of 52. He first draws a red card, places it back in the deck, shuffles the deck, and then draws another card. What is the probability of drawing a red card, placing it back in the deck, and drawing another red card? Answer choices are in the form of a percentage, rounded to the nearest whole number. 25% 22% 13% 4% RATIONALE Since Eric puts the card back and re-shuffles, the two events (first draw and second draw) are independent of each other. To find the probability of red on the first draw and second draw, we can use the following formula: Note that the probability of drawing a red card is or for each event. CONCEPT "And" Probability for Independent Events I need help with this question 8 A travel agency contacted a department store and obtained the list of all people who made purchases using their credit cards at the store in the last month. The agency then surveyed a random sample from the list, calling them to ask their preference for air travel or train travel for taking holidays. Which of the following types of bias affects the conclusions of the survey? Non-response bias Deliberate bias Selection bias Response bias RATIONALE Selection bias is when the mode of selection introduces a bias in the sample so that it is not representative of the population of interest. Since they only collected information from those using their credit card at a department store, this does not represent how people travel in general and is therefore an example of selection bias. CONCEPT Selection and Deliberate Bias I need help with this question 9 Jenae is able to purchase a different brand of coffee for half the price from a new supplier. She anticipated that her co-workers would object to switching to the new brand, as they were really partial to the coffee they have been drinking so far. Indeed, when offered a taste test of the old brand versus the new brand, her co-workers unanimously rejected the new brand. Jenae's boss, Steven, pointed out that this result was most likely due to the fact that the taste test was not . randomized blinded controlled replicated RATIONALE Since they didn't keep the participants unaware of what brand they were tasting, this could influence the findings. So, the rejection of the new brand was likely due to not blinding them from what brand they were drinking. CONCEPT Blinding I need help with this question 10 Fred Anderson, an artist, has recorded the number of visitors who visited his exhibit in the first 8 hours of opening day. He has made a scatter plot to depict the relationship between the number of hours and the number of visitors. How many visitors were there during the fourth hour? 1 21 4 20 RATIONALE The number of visitors at 4 hours is 4 visitors. This is the value that is directly at the value at 4 on the horizontal axis. CONCEPT Scatterplot I need help with this question 11 The third quartile (Q3) value from this box plot is . 37 29 48 60 RATIONALE The value for Q3 is the right edge of the box, which in this figure is 48. CONCEPT Five Number Summary and Boxplots I need help with this question 12 Shawna reads a scatterplot that displays the relationship between the number of cars owned per household and the average number of citizens who have health insurance in neighborhoods across the country. The plot shows a strong positive correlation. Shawna recalls that correlation does not imply causation. In this example, Shawna sees that increasing the number of cars per household would not cause members of her community to purchase health insurance. Identify the lurking variable that is causing an increase in both the number of cars owned and the average number of citizens with health insurance. The number of citizens in the United States Average mileage per vehicle The number of cars on the road Average income per household [Show Less]
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