MATH 225N Statistics Final Exam
1/1 POINTS
A fitness center claims that the mean amount of time that a person spends at the gym per visit is 33 minutes. ... [Show More] Identify the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter μ.
That is correct!
H0: μ≠33; Ha: μ=33 H0: μ=33; Ha: μ≠33
H0: μ≥33; Ha: μ<33 H0: μ≤33; Ha: μ>33
Answer Explanation
Correct answer:
Let the parameter μ be used to represent the mean. The null hypothesis is always stated with some form of equality: equal (=), greater than or equal to (≥), or less than or equal to (≤). Therefore, in this case, the null hypothesis H0 is μ=33. The alternative hypothesis is contradictory to the null hypothesis, so Ha is μ≠33.
QUESTION 2 1/1 POINTS
The answer choices below represent different hypothesis tests. Which of the choices are right-tailed tests? Select all correct answers.
That is correct!
•
H0:X≥17.1, Ha:X<17.1
H0:X=14.4, Ha:X≠14.4
H0:X≤3.8, Ha:X>3.8
H0:X≤7.4, Ha:X>7.4
H0:X=3.3, Ha:X≠3.3
•
Answer Explanation
Correct answer:
Remember the forms of the hypothesis tests.
• Right-tailed: H0:X≤X0, Ha:X>X0.
• Left-tailed: H0:X≥X0, Ha:X7.4
• H0:X≤3.8, Ha:X>3.8
QUESTION 3
0/1 POINTS
Find the Type II error given that the null hypothesis, H0, is: a building inspector claims that no more than 15% of structures in the county were built without permits.
That's not right.
The building inspector thinks that no more than 15% of the structures in the county were built without permits when, in fact, no more than 15% of the structures really were built without permits.
The building inspector thinks that more than 15% of the structures in the county were built without permits when, in fact, more than 15% of the structures really were built without permits.
The building inspector thinks that more than 15% of the structures in the county were built without permits when, in fact, at most 15% of the structures were built without permits.
The building inspector thinks that no more than 15% of the structures in the county were built without permits when, in fact, more than 15% of the structures were built without permits.
Answer Explanation
Correct answer:
A Type II error is the decision not to reject the null hypothesis when, in fact, it is false. In this case, the Type II error is when the building inspector thinks that no more
than 15% of the structures were built without permits when, in fact, more than 15% of the structures were built without permits.
Your answer:
Content attribution- Opens a dialog
QUESTION 4 1/1 POINTS
Suppose a chef claims that her meatball weight is less than 4 ounces, on average.
Several of her customers do not believe her, so the chef decides to do a hypothesis test, at a 10% significance level, to persuade them. She cooks 14 meatballs. The mean weight of the sample meatballs is 3.7 ounces. The chef knows from experience that the standard deviation for her meatball weight is 0.5 ounces.
• H0: μ≥4; Ha: μ<4
• α=0.1 (significance level)
What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places?
That is correct!
$$Test statistic = −2.24
Answer Explanation
Correct answers:
• $\text{Test statistic = }-2.24$Test statistic = −2.24
The hypotheses were chosen, and the significance level was decided on, so the next
step in hypothesis testing is to compute the test statistic. In this scenario, the sample mean weight, x¯=3.7. The sample the chef uses is 14 meatballs, so n=14. She knows the standard deviation of the meatballs, σ=0.5. Lastly, the chef is comparing the population mean weight to 4 ounces. So, this value (found in the null and alternative hypotheses) is μ0. Now we will substitute the values into the formula to compute the
test statistic:
z0=x¯−μ0σn√=3.7−40.514√≈−0.30.134≈−2.24
So, the test statistic for this hypothesis test is z0=−2.24.
QUESTION 5
1/1 POINTS
What is the p-value of a right-tailed one-mean hypothesis test, with a test statistic
of z0=1.74? (Do not round your answer; compute your answer using a value from the table below.) z1.51.61.71.81.90.000.9330.9450.9550.9640.9710.010.9340.9460.9560. 9650.9720.020.9360.9470.9570.9660.9730.030.9370.9480.9580.9660.9
730.040.9380.9490.9590.9670.9740.050.9390.9510.9600.9680.9740.06
0.9410.9520.9610.9690.9750.070.9420.9530.9620.9690.9760.080.9430.
9540.9620.9700.9760.090.9440.9540.9630.9710.977
That is correct!
$$0.041
Answer Explanation
Correct answers:
• $0.041$0.041
The p-value is the probability of an observed value of z=1.74 or greater if the null
hypothesis is true, because this hypothesis test is right-tailed. This probability is equal to the area under the Standard Normal curve to the right of z=1.74.
A standard normal curve with two points labeled on the horizontal axis. The mean is labeled at 0.00 and an observed value of 1.74 is labeled. The area under the curve and to the right of the observed value is shaded.
Using the Standard Normal Table, we can see that the p-value is equal to 0.959, which is the area to the left of z=1.74. (Standard Normal Tables give areas to the left.) So, the p-value we're looking for is p=1−0.959=0.041.
QUESTION 6 1/1 POINTS
Kenneth, a competitor in cup stacking, claims that his average stacking time
is 8.2 seconds. During a practice session, Kenneth has a sample stacking time mean of 7.8 seconds based on 11 trials. At the 4% significance level, does the data provide sufficient evidence to conclude that Kenneth's mean stacking time is less
than 8.2 seconds? Accept or reject the hypothesis given the sample data below.
• H0:μ=8.2 seconds; Ha:μ<8.2 seconds
• α=0.04 (significance level)
• z0=−1.75
• p=0.0401
That is correct!
Do not reject the null hypothesis because the p-value 0.0401 is greater than the significance level α=0.04.
Reject the null hypothesis because the p-value 0.0401 is greater than the significance level α=0.04.
Reject the null hypothesis because the value of z is negative. Reject the null hypothesis because |−1.75|>0.04.
Do not reject the null hypothesis because |−1.75|>0.04.
Answer Explanation
Correct answer:
In making the decision to reject or not reject H0, if α>p-value, reject H0 because the
results of the sample data are significant. There is sufficient evidence to conclude that H0 is an incorrect belief and that the alternative hypothesis, Ha, may be correct.
If α≤p-value, do not reject H0. The results of the sample data are not significant, so there is not sufficient evidence to conclude that the alternative hypothesis, Ha, may be correct. In this case, α=0.04 is less than or equal to p=0.0401, so the decision is to
not reject the null hypothesis.
QUESTION 7 1/1 POINTS
A recent study suggested that 81% of senior citizens take at least one prescription medication. Amelia is a nurse at a large hospital who would like to know whether the
percentage is the same for senior citizen patients who go to her hospital. She randomly selects 59 senior citizens patients who were treated at the hospital and finds that 49 of
them take at least one prescription medication. What are the null and alternative hypotheses for this hypothesis test?
That is correct!
{H0:p=0.81Ha:p>0.81
{H0:p≠0.81Ha:p=0.81
{H0:p=0.81Ha:p<0.81
{H0:p=0.81Ha:p≠0.81
Answer Explanation
Correct answer:
{H0:p=0.81Ha:p≠0.81
First verify whether all of the conditions have been met. Let p be the population proportion for the senior citizen patients treated at Amelia's hospital who take at least one prescription medication.
1. Since there are two independent outcomes for each trial, the proportion follows a binomial model.
2. The question states that the sample was collected randomly.
3. The expected number of successes, np=47.79, and the expected number of failures, nq=n(1−p)=11.21, are both greater than or equal to 5.
Since Amelia is testing whether the proportion is the same, the null hypothesis is
that p is equal to 0.81 and the alternative hypothesis is that p is not equal to 0.81. The null and alternative hypotheses are shown below.
{H0:p=0.81Ha:p≠0.81
QUESTION 8 1/1 POINTS
A researcher claims that the proportion of cars with manual transmission is less than 10%. To test this claim, a survey checked 1000 randomly selected cars. Of those cars, 95 had a manual transmission.
The following is the setup for the hypothesis test:
{H0:p=0.10Ha:p<0.10
Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places.
That is correct!
$$Test_Statistic=−0.53
Answer Explanation
Correct answers:
• $\text{Test_Statistic}=-0.53$Test_Statistic=−0.53
The proportion of successes is p^=951000=0.095. The test statistic is calculated as follows:
z=p^−p0p0⋅(1−p0)n−−−−−−√
z=0.095−0.100.10⋅(1−0.10)1000−−−−−−−−√ z≈−0.53
QUESTION 9 1/1 POINTS
A medical researcher claims that the proportion of people taking a certain medication that develop serious side effects is 12%. To test this claim, a random sample of 900 people taking the medication is taken and it is determined that 93 people have experienced serious side effects. .
The following is the setup for this hypothesis test:
H0:p = 0.12
Ha:p ≠ 0.12
Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places.
The following table can be utilized which provides areas under the Standard Normal Curve:
Answer Explanation
Correct answers:
• $\text{P-value=}0.124$P-value=0.124
Here are the steps needed to calculate the p-value for a hypothesis test for a proportion:
1. Determine if the hypothesis test is left tailed, right tailed, or two tailed.
2. Compute the value of the test statistic.
3. If the hypothesis test is left tailed, the p-value will be the area under the standard normal curve to the left of the test statistic z0
If the test is right tailed, the p-value will be the area under the standard normal curve to the right of the test statistic z0
If the test is two tailed, the p-value will be the area to the left of −|z0| plus the area to the right of |z0| under the standard normal curve
For this example, the test is a two tailed test and the test statistic, rounding to two decimal places, is z=0.1033−0.120.12(1−0.12)900−−−−−−−−−−−−√≈−1.54.
Thus the p-value is the area under the Standard Normal curve to the left of a z-score of
-1.54, plus the area under the Standard Normal curve to the right of a z-score of 1.54.
From a lookup table of the area under the Standard Normal curve, the corresponding area is then 2(0.062) = 0.124.
QUESTION 10 1/1 POINTS
An economist claims that the proportion of people who plan to purchase a fully electric vehicle as their next car is greater than 65%.
To test this claim, a random sample of 750 people are asked if they plan to purchase a fully electric vehicle as their next car Of these 750 people, 513 indicate that they do
plan to purchase an electric vehicle.
The following is the setup for this hypothesis test:
H0:p=0.65 Ha:p>0.65
In this example, the p-value was determined to be 0.026.
Come to a conclusion and interpret the results for this hypothesis test for a proportion (use a significance level of 5%.)
That is correct!
The decision is to reject the Null Hypothesis.
The conclusion is that there is enough evidence to support the claim.
The decision is to fail to reject the Null Hypothesis.
The conclusion is that there is not enough evidence to support the claim.
Answer Explanation
Correct answer:
To come to a conclusion and interpret the results for a hypothesis test for proportion using the P-Value Approach, the first step is to compare the p-value from the sample data with the level of significance.
The decision criteria is then as follows:
If the p-value is less than or equal to the given significance level, then the null hypothesis should be rejected.
So, if p≤α, reject H0; otherwise fail to reject H0.
When we have made a decision about the null hypothesis, it is important to write a thoughtful conclusion about the hypotheses in terms of the given problem's scenario.
Assuming the claim is the null hypothesis, the conclusion is then one of the following:
• if the decision is to reject the null hypothesis, then the conclusion is that there is enough evidence to reject the claim.
• if the decision is to fail to reject the null hypothesis, then the conclusion is that there is not enough evidence to reject the claim.
Assuming the claim is the alternative hypothesis, the conclusion is then one of the following:
• if the decision is to reject the null hypothesis, then the conclusion is that there is enough evidence to support the claim.
• if the decision is to fail to reject the null hypothesis, then the conclusion is that there is not enough evidence to support the claim.
In this example, the p-value = 0.026. We then compare the p-value to the level of significance to come to a conclusion for the hypothesis test.
In this example, the p-value is less than the level of significance which is 0.05.
Since the p-value is greater than the level of significance, the conclusion is to reject the null hypothesis.
QUESTION 11
1/1 POINTS
Becky's statistics teacher was teaching the class how to perform the z-test for a proportion. Becky was bored because she had already mastered the test, so she
decided to see if the coin she had in her pocket would come up heads or tails in a truly random fashion when flipped. She discretely flipped the coin 30 times and got
heads 18 times.
Becky conducts a one-proportion hypothesis test at the 5% significance level, to test whether the true proportion of heads is different from 50%.
Which answer choice shows the correct null and alternative hypotheses for this test?
That is correct!
H0:p=0.6; Ha:p>0.6, which is a right-tailed test.
H0:p=0.5; Ha:p<0.5, which is a left-tailed test. H0:p=0.6; Ha:p≠0.6, which is a two-tailed test. H0:p=0.5; Ha:p≠0.5, which is a two-tailed test.
Answer Explanation
Correct answer:
H0:p=0.5; Ha:p≠0.5, which is a two-tailed test.
The null hypothesis should be true proportion: H0:p=0.5. Becky wants to know if
the true proportion of heads is different from 0.5. This means that we just want to test if the proportion is not 0.5. So, the alternative hypothesis is Ha:p≠0.5, which is a two-
tailed test.
QUESTION 12 1/1 POINTS
John owns a computer repair service. For each computer, he
charges $50 plus $45 per hour of work. A linear equation that expresses the total amount of money John earns per computer is y=50+45x. What are the independent and dependent variables? What is the y-intercept and the slope?
That is correct!
The independent variable (x) is the amount of time John fixes a computer. The dependent variable (y) is the amount, in dollars, John earns for a computer.
John charges a one-time fee of $50 (this is when x=0), so the y-intercept is 50. John earns $45 for each hour he works, so the slope is 45.
The independent variable (x) is the amount, in dollars, John earns for a computer. The dependent variable (y) is the amount of time John fixes a computer.
John charges a one-time fee of $45 (this is when x=0), so the y-intercept is 45. John earns $50 for each hour he works, so the slope is 50.
The independent variable (x) is the amount, in dollars, John earns for a computer. The dependent variable (y) is the amount of time John fixes a computer.
John charges a one-time fee of $50 (this is when x=0), so the y-intercept is 50. John earns $45 for each hour he works, so the slope is 45.
The independent variable (x) is the amount of time John fixes a computer. The dependent variable (y) is the amount, in dollars, John earns for a computer.
John charges a one-time fee of $45 (this is when x=0), so the y-intercept is 45. John earns $50 for each hour he works, so the slope is 50.
Answer Explanation
Correct answer:
The independent variable (x) is the amount of time John fixes a computer because it is the value that changes. He may work different amounts per computer, and his earnings
are dependent on how many hours he works. This is why the amount, in dollars, John earns for a computer is the dependent variable (y).
The y-intercept is 50 (b=50). This is his one-time fee. The slope is 45 (a=45). This is the increase for each hour he works.
QUESTION 13 1/1 POINTS
Ariana keeps track of the amount of time she studies and the score she gets on her quizzes. The data are shown in the table below. Which of the scatter plots below accurately records the data?
Hours studying Quiz score
1 5
2 5
3 7
4 9
5 9
That is correct! [Show Less]
