A sample of 50 potential customers was asked to use your new product and the product of the leading competitor. After one week, they were asked to indicate which product they preferred. In the sample, 30 potential customers said that they preferred your product.
Answer the following questions by filling out the steps below.
A. Find the sample proportion estimate (the statistic).
B. Suppose you would launch your new product ONLY IF MORE THAN HALF (50%) of your customers would prefer it to the leading competitor. Perform the hypothesis testing (test of significance) to help you make your decision.
C. perform the hypothesis testing in part b, and then compute the 95% confidence interval
• Sample PROPORTION estimate (statistic): ?̅ = ?/n =_______________________
• Step 1: Hypotheses (???-TAILED) TEST): H0: p = p0 = 0.0 vs. HA: p < 0.50="" or="" p=""> 0.50 or p ≠ 0.50
(circle one) • ASSUME Ho IS TRUE: p = po = 0.50 •
???? = √ ?? ( ?− ?? ) ? = ____________________________________________________
• Step 2: Test Statistic: z = ?̅ − ?? ???? = ________________________________
• Step 3: p-value = P(Z _________ ) = ______________ (Use z-Table)
• Step 4: Conclusion: DO NOT REJECT H0 or REJECT H0 (circle one) •
Interpretation (circle one) based:
a. The percentage of customers who prefer your new product to the leading competitor is NOT “SIGNIFICANTLY” MORE THAN 50%; do not launch the new product.
b. The percentage of customers who prefer your new product to the leading competitor is “SIGNIFICANTLY” MORE THAN 50%; do not launch the new product.
• Important: If p-value is between 5% and 10, and α = 10%, then your conclusion may be different. So, if you still want to launch the new product, do the product testing again with a larger number of customers (larger sample size) to get a more definite yes or no.
• for the Significance test above: p-value = _________________________
• Find the 95% confidence interval (watch out: use 2-tailed test): CI = [ _________, ________]