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all merchandise purchased at department stores nationally is returned

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all merchandise purchased at department stores nationally is returned. Your store did a sample of 100 purchased items and found that 11 of the items were returned. You want to see if your store has a return rate that is significantly different from the national average with a significance level of 0.05.

1.      For each number in the problem, give the appropriate mathematical symbol associated with that number:

a. 6%=.06 =

 

b. 100 =

 

c.  11 =

 

d. .05 =

 

2.      What is the point estimate of the proportion of items returned at your store?

 

3.      State the null and alternative hypotheses.

 

4.      Compute the value of the test statistic.

 

5.      Find the p-value.

 

6.      What is your conclusion in statistical terms?

 

7.      What is your conclusion in business terms?

 

A CEO is trying to decide whether or not to fire the HR director. The default decision is for the HR director to keep the job, but the CEO will fire the HR director if there is statistically significant evidence that less than 75% of the new employees at the company stay for more than a year. A sample of 300 new employees showed that 72% of the new employees in the sample stayed for more than a year. 

8.       For each number in the problem, give the appropriate mathematical symbol associated with that number:

a. 75% = .75 =

 

b. 300 =

 

c.  72% = .72 =

9.       What are the null and alternative hypotheses?

10.  Specify α. (You choose a value that makes sense for this problem.)

 

11.  What is the value of the test statistic?

 

12.  What is the p-value?

 

13.  State your conclusion in statistical terms.

 

14.  What will the CEO do?