STAT 200: Introduction to Statistics Final Examination
1. The World Health Organization wishes to estimate the mean density of people per
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kilometer, they collect data on 56 countries. Justify for full credit.
(a) Which of the following is the variable?
(i) All countries in the world
(ii) Density of people per square kilometer
(iii) Set of densities of people per square kilometer of all countries
(iv) Set of densities of people per square kilometer of 56 countries
(b) Which of the following is the population?
(i) All countries in the world
(ii) Density of people per square kilometer
(iii) Set of densities of people per square kilometer of all countries
(iv) Set of densities of people per square kilometer of 56 countries
2. Choose the best answer. Justify for full credit.
(a) The hotel ratings are usually on a scale from 0 star to 5 stars. The level of this
measurement is
(i) interval
(ii) nominal
(iii) ordinal
(iv) ratio
(b) In a career readiness research, 100 students were randomly selected from the
psychology program, 150 students were randomly selected from the communications
program, and 120 students were randomly selected from cyber security program. This
type of sampling is called:
(i) cluster
(ii) convenience
(iii) systematic
(iv) stratified
3. True or False. Justify for full credit.
(a) If the variance from a data set is zero, then all the observations in this data set must be
identical.
(b) The median of a normal distribution curve is always zero.
4. A school district wanted to assess the effectiveness of a new math readiness program for fifth
graders. The school district is divided into the individual fifth grade classrooms and 10
classrooms are randomly selected. All of the children in each of the 10 selected classrooms are
assessed.
(a) What type of sampling method is being used?
(b) Please explain your answer.
5. A study was conducted to determine whether the mean braking distance of four-cylinder cars
is greater than the mean braking distance of six-cylinder cars. A random sample of 20 fourcylinder cars and a random sample of 20 six-cylinder cars were obtained, and the braking
distances were measured.
(a) What would be the appropriate hypothesis test for this analysis?
(i) t-test for two independent samples
(ii) t-test for dependent samples
(iii) z-test for population mean
(iv) correlation
(b) Explain the rationale for your selection in (a). Specifically, why would this be the
appropriate statistical approach?
6. A study of 10 different weight loss programs involved 500 subjects. Each of the 10 programs
had 50 subjects in it. The subjects were followed for 12 months. Weight change for each subject
was recorded. The researcher wants to test the claim that all ten programs are equally effective in
weight loss.
(a) Which statistical approach should be used?
(i) confidence interval
(ii) t-test
(iii) ANOVA
(iv) Chi square
(b) Explain the rationale for your selection in (a). Specifically, why would this be the
appropriate statistical approach?
7. A STAT 200 professor took a sample of 10 midterm exam scores from a class of 30 students.
The 10 scores are shown in the table below:
(a) What is the sample mean?
(b) What is the sample standard deviation? (Round your answer to two decimal places)
(c) If you leveraged technology to get the answers for part (a) and/or part (b), what
technology did you use? If an online applet was used, please list the URL, and describe
the steps. If a calculator or Excel was used, please write out the function.
8. UMUC Stat Club must appoint a president, a vice president, and a treasurer. There are 10
qualified candidates.
(a) How many different ways can the officers be appointed?
(b) Please describe the method used and the reason why it is appropriate for answering
the question. Just the answer, without the description and reason, will receive no credit.
9. Sara has eight new summer outfits. She plans to pack three of the new summer outfits in her
trip to Tokyo.
(a) How many different ways can the three summer outfits be selected?
(b) Please describe the method used and the reason why it is appropriate for answering
the question. Just the answer, without the description and reason, will receive no credit.
10. There are 4 suits (heart, diamond, clover, and spade) in a 52-card deck, and each suit has 13
cards. Suppose your experiment is to draw one card from a deck and observe what suit it is.
Express the probability in fraction format. (Show all work. Just the answer, without supporting
work, will receive no credit.)
(a) Find the probability of drawing a heart or diamond.
(b) Find the probability that the card is not a spade.
11. An airline company has a policy of routinely overbooking flights. The following probability
distribution table shows the random variable, x, where x is number of passengers who cannot be
boarded because there are more passengers than seats:
(a) Determine the mean of x (Round the answer to two decimal places). Show all work.
Answers without supporting work will not receive credit.
(b) Determine the standard deviation of x. (Round the answer to two decimal places)
Show all work. Answers without supporting work will not receive credit.
12. Max Scherzer, the starting pitcher for the Nationals, on average, has a 0.250 probability of
hitting the ball in a single "at bat". In one game, he gets 6 "at bats."
(a) Let X be the number of hits that Max gets. As we know, the distribution of X is a
binomial probability distribution. What is the number of trials (n), probability of
successes (p) and probability of failures (q), respectively?
(b) Find the probability that he gets at least 3 hits in the one game. (Round the answer to
3 decimal places) Show all work. Just the answer, without supporting work, will receive
no credit.
13. Assume that gas mileage for cars is normally distributed with a mean of 23.5 miles per gallon
and a standard deviation of 10 miles per gallon. Show all work. Just the answer, without
supporting work, will receive no credit.
(a) What is the probability that a randomly selected car gets between 15 and 30 miles per
gallon? (Round the answer to 4 decimal places)
(b) Find the 75th percentile of the gas mileage distribution. (Round the answer to 2
decimal places)
14. Based on the performance of all individuals who tested between 2015 and 2017, the GMAT
total scores are normally distributed with a mean of 561.27 and a standard deviation of 119.31.
(https://www.gmac.com/gmat-other-assessments/accessing-gmat-exam-scores-and-reports/gmatscoring-by-exam-section-normal-view#tab5). Show all work. Just the answer, without supporting
work, will receive no credit.
(a) For a sample of size 100, state the standard deviation of the sample mean (the
"standard error of the mean"). (Round your answer to three decimal places)
(b) Suppose a sample of size 100 is taken. Find the probability that the sample mean
GMAT total scores is more than 575. (Round your answer to three decimal places)
15. A survey showed that 980 of the 1500 adult respondents believe in global warming.
(a) Construct a 99% confidence interval estimate of the proportion of adults believing in
global warming. (Round the lower bound and upper bound of the confidence interval to
three decimal places) Include description of how confidence interval was constructed.
(b) Describe the results of the survey in everyday language.
16. In a study to assess the effectiveness of garlic for lowering cholesterol, 50 adults were treated
with garlic tablets. Cholesterol levels were measured before and after treatment. The changes in
their LDL cholesterol (in mg/dL) have a mean of 8 and a standard deviation of 4.
(a) Construct a 95% interval estimate of the mean change in LDL cholesterol after the
garlic tablet treatment. (Round the lower bound and upper bound of the confidence
interval to two decimal places) Include description of how confidence interval was
constructed.
(b) Describe the results of the study in everyday language.
17. The UMUC Daily News reported that the color distribution for plain M&M’s was: 40%
brown, 20% yellow, 20% orange, 10% green, and 10% tan. Each piece of candy in a random
sample of 100 plain M&M’s was classified according to color, and the results are listed below.
Use a 0.05 significance level to test the claim that the published color distribution is correct.
Show all work and justify your answer.
(a) What is the appropriate hypothesis test: z-test for sample proportion, t-test for sample
mean, chi-square goodness of fit test, F-test for ANOVA? Please identify and explain
why it is appropriate for analyzing this data.
(b) Identify the null hypothesis and the alternative hypothesis.
(c) Determine the test statistic. Round your answer to two decimal places. Show all work;
writing the correct test statistic, without supporting work, will receive no credit.
(d) Determine the P-value. Round your answer to two decimal places. Show all work;
writing the correct P-value, without supporting work, will receive no credit.
(e) Compare p-value and significance level α. What decision should be made regarding
the null hypothesis (e.g., reject or fail to reject) and why?
(f) Is there sufficient evidence to support the claim that the published color distribution is
correct? Justify your answer.
18. In a study of memory recall, 5 people were given 10 minutes to memorize a list of 20 words.
Each was asked to list as many of the words as he or she could remember both 1 hour and 24
hours later. Does the data below suggest that the mean number of words recalled after 1 hour
exceeds the mean recall after 24 hours? Assume we want to use a 0.05 significance level to test
the claim.
(a) What is the appropriate hypothesis test to use for this analysis? Please identify and
explain why it is appropriate.
(b) Let μ1 = mean words recalled after 1 hour. Let μ2 = mean words recalled after 24
hours. Which of the following statements correctly defines the null hypothesis?
(i) μ1 - μ2 > 0 (μd > 0)
(ii) μ1 - μ2 = 0 (μd = 0)
(iii) μ1 - μ2 < 0 (μd < 0)
(c) Let μ1 = mean words recalled after 1 hour. Let μ2 = mean words recalled after 24
hours. Which of the following statements correctly defines the alternative hypothesis?
(i) μ1 - μ2 > 0 (μd > 0)
(ii) μ1 - μ2 = 0 (μd = 0)
(iii) μ1 - μ2 < 0 (μd < 0)
(d) Determine the test statistic. Round your answer to three decimal places. Describe
method used for obtaining the test statistic.
(e) Determine the p-value. Round your answer to three decimal places. Describe method
used for obtaining the p-value.
(f) Compare p-value and significance level α. What decision should be made regarding
the null hypothesis (e.g., reject or fail to reject) and why?
(g) What do the results of this study tell us about the mean number of words recalled after
1 hours and after 24 hours? Justify your conclusion.
19. A grocery store manager is interested in testing the claim that banana is the favorite fruit for
more than 50% of the adults. The manager conducted a survey on a random sample of 100
adults. The survey showed that 56 adults in the sample chose banana as his/her favorite fruit.
Assume the manager wants to use a 0.05 significance level to test the claim.
(a) What is the appropriate hypothesis test to use for this analysis? Please identify and
explain why it is appropriate.
(b) Identify the null hypothesis and the alternative hypothesis.
(c) Determine the test statistic. Round your answer to two decimal places. Describe
method used for obtaining the test statistic.
(d) Determine the p-value. Round your answer to three decimal places. Describe method
used for obtaining the p-value.
(e) Compare p-value and significance level α. What decision should be made regarding
the null hypothesis (e.g., reject or fail to reject) and why?
(f) Is there sufficient evidence to support the claim that banana is the favorite fruit for
more than 50% of the adults? Explain your conclusion.
20. A scientist believes that the frequency of cricket chirping is a good predictor of the ambient
temperature. A random sample produced the following data where x is the number of cricket
chirps in one minute and y is the ambient temperature in Fahrenheit.
(a) Find an equation of the least squares regression line. Round the slope and y-intercept
value to two decimal places. Describe method for obtaining results.
(b) Based on the equation from part (a), what is the predicted temperature when a cricket
chirps 300 times in one minute? Show all work and justify your answer.
(c) Based on the equation from part (a), what is the predicted temperature when a cricket
chirps 140 times in one minute? Show all work and justify your answer.
(d) Which predicted temperature that you calculated for (b) and (c) do you think is closer
to the true temperature and why? [Show Less]
