Answer to Question #99842 in Statistics and Probability for Juliet Beglaryan

Question

A study by Consumer Reports showed that 64% of supermarket shoppers believe supermarket brands to be as good as national name brands. To investigate whether this result applies to its own store, the manager of the Publix in Clemson, SC asked a random sample of 100 shoppers whether they believed that supermarket brand ketchup was as good as the national brand ketchup, 52 believed the did believe the supermarket brand was as good as the national brand or not. Let a=.10

Answer 1

Null hypothesis $H_0:p=0.64$

Alternative hypothesis $H_a:p\ne0.64$

Test statistic: $z=\frac{0.52-0.64}{\sqrt{\frac{0.64(1-0.64)}{100}}}=-2.5$

P-value: $p=2P(Z<-2.5)=0.012.$

Since the P-value is less than 0.1, reject the null hypothesis.

There is a significant evidence that the Customer Reports result does not apply to the manager's own store.