Mark the letter T or F next to each statement to indicate whether it is a true claim or a false one.

1.The test statistics for a 90% confidence interval and a two-tailed hypothesis test conducted at a significance level of 10% using the same set of data will be identical.

2.According to the central limit theorem, large populations of data are approximately normally distributed.

3.A finite population correction factor should be incorporated into standard error calculations if the sample comprises less than 5% of the original population.

4.Calculate the minimum number of items to sample when constructing a 95% confidence interval for a mean. Assume the population standard deviation is 6 and the margin of error should be no bigger than 2.

A. 30 B. 35 C. 40 D. 45

5.Consider drawing a sample of 25 items from a normally distributed population with a standard deviation of 10 and a mean of 50. Calculate the probability that the SAMPLE MEAN is less than 47.

A. 0.4332 B. 0.5668 C. 0.0668 D. 0.1336

6.Which of the following is a property of the sampling distribution of the sample mean (i.e. the population of sample means for a given size)?

A. The population of samples is approximately normally distributed.

B. The mean for a population of samples is the same as the mean for the original population from which they were taken.

C. The standard deviation for a population of samples is smaller than the standard deviation for the original population from which they were taken.

D. All of the above.

7.Consider Welch's t-test (2-sample t-test comparing means with unequal variances). Given the following information, calculate the degrees of freedom. S1=8, n1=16, S2=12, n2=48

A. 38 B. 45 C. 62 D. 63

8.Over a sample of 64 exams, Joel has spent an average of 10 minutes marking each exam with a standard deviation of 3 minutes. Suppose you want to construct a confidence interval for the average time Joel spends marking an exam.

a. When calculating the margin of error, will you use a z statistic or a t statistic? Explain how you chose. The space provided is not indicative of how long your response should be.

b. Assuming a 98% level of confidence, report the NUMERICAL z or t statistic. You do not need to show any work.

c. Construct the confidence interval.

d. Briefly interpret your confidence interval by carefully explaining what information it reveals and what it means to be 98% confident in your result.

9.Consider a 1-sample t-test for a population mean. The test is being conducted with a 2-sided alternative hypothesis and a significance level of 10%. Which of the following statements is true?

A. Given that H0 is true, the risk of a false positive result is 10%.

B. This test will yield the same inferences as constructing a 90% confidence interval.

C. Given that H0 is true, each rejection region spans 5% of the possible test results (t statistics).

D. All of the above.

10.Calculate the minimum number of items to sample when constructing a 99% confidence interval for a proportion. Suppose that the population proportion is assumed to be 0.60 and the margin of error should be no bigger than 0.05.

A. 260 B. 640 C. 1,040 D. 369

11.Consider a population of 100 items with a standard deviation of 10. Suppose that all possible samples of size 25 are to be drawn from the population. Calculate the standard error.

A. 0.88 B. 1.00 C. 1.74 D. 2.30

12.Which of the following best describes the central limit theorem (CLT)?

A. The mean for a population of samples is the same as the mean for the original population from which they were taken.

B. The standard deviation for a population of samples is smaller than the standard deviation for the original population from which they were taken.

C. The population of samples is approximately normally distributed.

D. All of the above

13.Consider Welch's t-test (2-sample t-test comparing means with unequal variances). Given the following information, calculate the degrees of freedom. S1=10, n1=20, S2=5, n2=25

A. 26 B. 33 C. 27 D. 21

14.Consider an 84% confidence interval constructed from a standard normal distribution. Report the z-statistic used to calculate the margin of error.

A. 0.16 B. 0.30 C. 1.41 D. 1.28

15.Over a sample of 25 full tanks of gasoline, Joel has averaged 18.2 miles per gallon (MPG) with a standard deviation of 1.4 MPG. Suppose you have been asked to construct a confidence interval for Joel's average fuel economy.

a. When calculating the margin of error, will you use a z or a t distribution? Explain how you chose.

b. Assuming a 90% level of confidence, report the NUMERICAL z or t statistic.

c. Construct the confidence interval

d. Briefly interpret your confidence interval by carefully explaining what information it reveals and what it means to be 90% confident in your result.

16.In a sample of 200 students, 112 received grades higher than a B-. At a 10% significance level, is there enough statistical evidence to support a claim that B- is the median grade received by all students?

i. State the null and alternative hypotheses

ii. The significance level for this test is 10% ( = 0.10)

iii. 1 Sample z-test for a population proportion

iv. Specify the decision rule

Calculate the zsample Statistic

Calculate the sample p-value

17.In a sample of 14 students who stayed up all night to study for an exam the average grade was 68% with a standard deviation of 8%. A sample of 12 students who wrote the same exam after a good night's sleep received an average grade of 75% with a standard deviation of 7%. At a 5% significance level, is there enough statistical evidence to support a claim that students who get a good night's sleep perform better on average?

i. State the null and alternative hypotheses

ii. The significance level for this test is 5% ( = 0.05)

iii. 2-sample pooled variance t-test comparing population means

iv. Specify the decision rule

Calculate the SP 2 Statistic

Calculate the tsample Statistic

Calculate the sample p-value

The table below records the race times for a sample of 10 college sprinters before and after taking an experimental performance enhancing drug.

Athlete Ben Lance Luiza Marion Maria Barry Tyson Ross Johann Alex

Before 10.2 24.3 12.1 45.8 15.0 43.7 10.9 39.3 10.7 11.3

After 9.5 22.7 11.8 44.2 14.8 43.9 10.3 41.0 10.0 9.4

a. Construct the distribution of differences by calculating the change in each athlete's race time.

b. Calculate the mean change in race times.

c. Calculate the standard deviation for the change in race times.

d. At a 1% significance level, is there enough statistical evidence to support a claim that the drug is effective at improving athletic performance?

i. State the null and alternative hypotheses.

ii. The significance level for this test is 1% ( = 0.01)

iii. 2 sample paired t-test comparing population means

iv. Specify the decision rule.

v. Perform the test.