Question

1. Academy Sports & Outdoors is interested in the difference in the proportions of returned purchases at2 different locations, retail stores in Dallas and Houston. They have collected the following data. Refer to the Dallas store as Population 1 and the Houston store as Population 2, and answer the following questions leading up to the hypothesis test.

                         Dallas store (population 1)                                   Houston store (population 2)

                   Goods purchased last month = 2,144                     Goods purchased last month = 3,509

               Number of these that were returned = 150        Number of these that were returned = 140

H₀ : ¯p₁− p¯₂ = 0

H_a : ¯p₁− p¯₂ 6= 0

1. What is the estimate of the proportion in population 1?
2. What is the estimate of the proportion in population 2?        
3. What is the estimate of the difference between the two populationproportions?          
4. What is the standard error of the difference between the twopopulation proportions? Round to 4 decimal places.
5. Develop a 90% confidence interval for the difference between the twopopulation proportions.               
6. Develop a 95% confidence interval for the difference between the twopopulation proportions.               
7. Develop a 99% confidence interval for the difference between the twopopulation proportions.
8. What is the pooled estimate of p?
9. What is the test statistic (z-value)? Round to 2 decimal places.
10. What is the p-value? Round to 4 decimal places.
11. With a 90% confidence level (α = 0.10), what is your conclusion?
12. With a 95% confidence level (α = 0.05), what is your conclusion?
13. With a 99% confidence level (α = 0.01), what is your conclusion?

Answer 1

a. What is the estimate of the proportion in population 1?

P1 = 150 /2144 = 0.07

                  

b. What is the estimate of the proportion in population 2?  

P2 =140/3509 = 0.04

h) What is the pooled estimate of p?

i.What is the test statistic (z-value)?

j.What is the p-value?

The p-value is p = 0

k.With a 90% confidence level (α = 0.10), what is your conclusion?

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population proportion p1​ is different than p2​, at the 0.10 significance level.

l.With a 95% confidence level (α = 0.05), what is your conclusion?

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population proportion p1​ is different than p2​, at the 0.05 significance level.

m.With a 99% confidence level (α = 0.01), what is your conclusion?

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population proportion p1​ is different than p2​, at the 0.05 significance level.