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1) A major DVD rental chain is considering opening a new store in an area that currently does not have any such stores.

1) A major DVD rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with DVD players. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have DVD players.

a) State the null hypothesis and the alternative hypothesis.

b) What is the value of the test statistic in this problem? Explain how you obtain your answer.

c) What is the p-value associated with the test statistic in this problem? Explain how you obtain your answer.

d) Using a 3% level of significance, what would be your decision in the hypothesis test? Justify your answer.

e) Should the rental chain's open a new store based on the hypothesis test using a 3% level of significance? Justify your answer.


2) You are given the following information:

s12 = 4     s22 = 6

n1 = 16     n2 = 25

a) Calculate the degrees of freedom that should be used in the pooled-variance t test. Show how you obtain your answer.

b) Calculate sp2, the pooled sample variance that should be used in the pooled-variance t test. Show how you obtain your answer.


3) A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. Analysis of the mean salaries of the females and males in the sample is given below. Suppose the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. 

Hypothesized Difference

0

Level of Significance

0.05

Population 1 Sample

Sample Size

18

Sample Mean

48266.7

Sample Standard Deviation

13577.63

Population 2 Sample

Sample Size

12

Sample Mean

55000

Sample Standard Deviation

11741.29

Difference in Sample Means

-6733.3

t-Test Statistic

-1.40193

Lower-Tail Test

Lower Critical Value

-1.70113

p-Value

0.085962


a) According to the test run, state an appropriate alternative hypothesis.

b) From the analysis in Table 10-2, what is the correct test statistic? Explain how you obtain your answer.

c) What is the 95% confidence interval estimate for the difference between two means? Show how you obtain your answer.

d) What conclusion do you reach for this test? Explain how you obtain your answer.

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