Question

A program was created to randomly choose customers at a shoe store to receive a discount. The program claims 15% of the receipts will get a discount in the long run. The manager of the shoe store is skeptical and believes the program's calculations are incorrect. She selects a random sample and finds that 12% received the discount. The confidence interval is 0.12 ± 0.05 with all conditions for inference met.

Part A: Using the given confidence interval, is it statistically evident that the program is not working? Explain.


Part B: Is it statistically evident from the confidence interval that the program creates the discount with a 0.15 probability? Explain.


Part C: Another random sample of receipts is taken. This sample is six times the size of the original. Twelve percent of the receipts in the second sample received the discount. What is the value of margin of error based on the second sample with the same confidence level as the original interval?


Part D: Using the margin of error from the second sample in part C, is the program working as planned? Explain.

Answer 1

A: There is no statistical evidence that the program is not working as intended because 0.15 is between the range of 0.12 ± 0.05 = (0.07,0.17)

B: 0.15 is between the range of (0.07,0.17) so it is statistically probable.

C: margin of error=0.05/((6)^(1/2))=0.0204

D: No the program is not working as planned because 0.15 is not within the range of 0.12±0.0204=(0.0996,0.1404)

Explanation:

Within the answer. please tell me if I am wrong