Question

Consider a consumer satisfaction survey conducted by A1 Retailers in which consumers respond that they are either satisfied or not satisfied. From all the customers that purchased products in a given week, only 144 surveys were completed. In this sample, 65% of customers indicated they were satisfied. Perform a test of hypothesis that the satisfaction rate among all customers is greater than 70% with a Type I Error of 0.02.

Answer 1

Here we have to test that

where

n = 144

Sample proportion =

Test statistic:

z = -1.31 (Round to 2 decimal)

Test statistic = -1.31

alpha = 0.02

Test is one tailed (Right tailed) test.

P value = P(z > -1.31)

= 1 - P(z < -1.31)

= 1 - 0.0951 (From statistical table of z values)

= 0.9049

P value = 0.9049

Here p value > alpha

So we fail to reject H0.

Conclusion: Ther is insufficient evidence to conclude that the satisfaction rate among all customers is greater than 70%.