The Energy Information Administration reported that51.7%of homes in the United States were heated by natural gas. A random sample of212homes found that115were heated by natural gas. Does the evidence support the claim, or has the percentage changed? Use = 0.01and theP-value method.

(a) State the hypotheses and identify the claim with the correct hypothesis.

H₀ : p ____ 0.517

H₁ : p ____ 0.517

Which above is the claim?

This hypothesis test is a_____- tailed test.

(b) Compute the test value. Round the sample proportion to three decimal places andzscore value to two decimal places.

(c) Find theP-value. Round the answer to four decimal places.

(d) Make the decision.

_____the null hypothesis.

(e) Summarize the results.

There_______enough evidence to reject the claim that51.7%of homes in the United States were heated by natural gas.

(f) Would the percentage of homes heated by natural gas change, if the sample were taken in a different geographic area?

______, the percentage of homes heated by natural gas________change, if the sample were taken in a different geographic area.