Question

A dry cleaning store is considering opening a new store in an area that currently does not have such store. There is evidence more than 5,000 of 20,000 households in the area have dry cleaning needs. it conducts a telephone poll of 300 randomly selectedd households in the area and finds that 96 have strong interest. The owner's conclusion from the hypothessis test using a 5% level of significance is:

A to open a new store

B not to open an new store

C to delay opening a new store untill addiitonal evidence is collected

D we cannot tell what the decision should be from the information given

Answer 1

Let p be the true proportion of households in the area have dry cleaning needs and have strong interest.

Claim is that p > 5000/20000 = 0.25

Null Hypothesis H0: p = 0.25

Alternative Hypothesis H1: p > 0.25

Sample proportion, = 96 / 300 = 0.32

Standard error of proportion if null hypothesis is true, SE = = 0.025

Test statistic, z = ( - p) / SE

= (0.32 - 0.25) / 0.025

= 2.8

P-value = P(z > 2.8) = 0.0026

Since p-value is less than 0.05 significance level, we reject null hypothesis H0 and conclude that there is significant evidence that proportion of households in the area having dry cleaning needs and have strong interest is greater than 0.25.

Thus, the owner's conclusion from the hypothesis test using a 5% level of significance is:

A to open a new store