Question

home / study / math / statistics and probability / statistics and probability questions and answers / Sample Question: A Major DVD Rental Chain Is Considering Opening A New Store In An Area That ...

Question: Sample question: A major DVD rental chain is considering opening a new store in an area that curr...

Sample question:

A major DVD rental 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 are equipped with DVD players. It conducts a telephone

poll of 300 randomly selected households in the area and finds that 96 have DVD players.

The decision on the hypothesis test using a 5% level of significance is...

A) to accept H0 in favor of H1.

B) to reject H0 in favor of H1.

C) to fail to reject H0 in favor of H1.

D) We cannot tell what the decision should be from the information given.

show work so I can understand thanks

Answer 1

The chain will open if

This means the null and alternative hypothesis are:

Now, the test statistics is given by

Where,

Assuming the null hypothesis is true, the test statistics is

As this is a right tailed test, for 5% level of significance the critical value of z-distribution is 1.645.

As the test statistics is greater than the critical value, hence it lies in the rejection region.

Hence, we have sufficient evidence to reject H₀ in favour of H₁.