A pizza chain is considering opening a new store in an area that currently does

Question

A pizza chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area have a favorable view of its chain. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have a favorable view. The decision on the hypothesis test using a 5% level of significance is: Select one: A. to fail to reject Ho in favor of H_s. B. to reject H_0 in favor of H_1 C. to accept H_0 in favor of H_1. D. We cannot tell what the decision should be from the information given:

Explanation / Answer

here null hypothesis : p=5000/20000=0.25

alterbate hypothesis:p>0.25

n=300 ; p=0.25

std error =(p(1-p)/n)1/2 =0.025

phat=96/300 =0.32

hence test stat z=(phat-p)/std error =2.8

for above test stat p value =0.0026

as p value is less then 0.05 level of significance; therefore

option B is correct

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