Question

A researcher claims that the proportion of smokers in a certain city is less than 20%. To test this claim, a random sample of 700 people is taken in the city and 150 people indicate they are smokers.

The following is the setup for this hypothesis test:

H0:p=0.20

Ha:p<0.20

In this example, the p-value was determined to be 0.828.

Come to a conclusion and interpret the results for this hypothesis test for a proportion (use a significance level of 5%)

Ans:

The decision is to fail to reject the Null Hypothesis.

The conclusion is that there is not enough evidence to support the claim.

Question

A researcher claims that the incidence of a certain type of cancer is less than 5%. To test this claim, the a random sample of 4000 people are checked and 170 are determined to have the cancer.

The following is the setup for this hypothesis test:

H0:p=0.05

Ha:p<0.05

In this example, the p-value was determined to be 0.015.

Come to a conclusion and interpret the results for this hypothesis test for a proportion (use a significance level of 5%)