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1) Determine whether each statement is "true" or "false" and explain why. a) "A statistics professor wanted to test whether the grades on a...

1) Determine whether each statement is “true” or “false” and explain why.

a) “A statistics professor wanted to test whether the grades on a statistics test were the same for upper and lower classmen. The professor took a random sample of size 10 from each, conducted a test and found out that the variances were equal. For this situation, the professor should use a t test with related samples.”

b) “A statistics professor wanted to test whether the grades on a statistics test were the same for upper and lower classmen. The professor took a random sample of size 10 from each, conducted a test and found out that the variances were equal. For this situation, the professor should use a t test with independent samples.”

c) “Marine drill instructor recorded the time in which each of 11 recruits completed an obstacle course both before and after basic training. To test whether any improvement occurred, the instructor would use a t-distribution with 11 degrees of freedom.”

d) “A Marine drill instructor recorded the time in which each of 11 recruits completed an obstacle course both before and after basic training. To test whether any improvement occurred, the instructor would use a t-distribution with 10 degrees of freedom.”


2) A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let π1 and π2 represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively.

a) If the firm wanted to test whether this proportion has changed from the previous study, which represents the relevant hypotheses?

    A) H0 : π1 - π2 = 0 versus H1: π1 - π2 ≠ 0

    B) H0 : π1 - π2 ≠ 0 versus H1 : π1 - π2 = 0

   C) H0 : π1 - π2 ≤ 0 versus H1 : π1 - π2 > 0

   D) H0 : π1 - π2 ≥ 0 versus H1 : π1 - π2 < 0

b) What is the unbiased point estimate for the difference between the two population proportions? Explain how you obtain your answer.

c) What is/are the critical value(s) when performing a Z test on whether population proportions are different if α = 0.05? Explain how you obtain your answer.

d) What is the estimated standard error of the difference between the two sample proportions? Show how you obtain your answer.

e) Construct a 95% confidence interval estimate of the difference in proportion of workers who would like to attend a self-improvement course in the recent study and the past study. Show how you obtain your answer.

f)  The company tests to determine at the 0.05 level whether the population proportion has changed from the previous study. Which would be the conclusion? Explain how you obtain your answer.


3) The amount of time required to reach a customer service representative has a huge impact on customer satisfaction.  Below is the Excel output from a study to see whether there is evidence of a difference in the mean amounts of time required to reach a customer service representative between two hotels. Assume that the population variances in the amount of time for the two hotels are not equal. 

t-Test: Two-Sample Assuming Unequal Variances

Hotel 1

Hotel 2

Mean

2.214

2.0115

Variance

2.951657

3.57855

Observations

20

20

Hypothesized Mean Difference

0

df

38

t Stat

0.354386

P(T<) one-tail

0.362504

t Critical one-tail

1.685953

P(T<) two-tail

0.725009

t Critical two-tail

2.024394


a) State the null and alternative hypotheses for testing if there is evidence of a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels.

b) What is the value of the test statistic for testing if there is evidence of a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels? Explain how you obtain your answer.

c) What is the critical value for testing if there is evidence of a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels at the 5% level of significance? Explain how you obtain your answer.

d) Suppose α = 0.05. Which of the following represents the correct conclusion for a test on a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels? Show how you obtain your answer.

    A) There is no evidence of a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels.

    B) There is evidence of a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels.

    C) There is no evidence that the variabilities of the amount of time required to reach a customer service representative between the two hotels are the same.

    D) There is evidence that the variabilities of the amount of time required to reach a customer service representative between the two hotels are the same.

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