Natural Gas HeatThe Energy Information Administration reported that51.7%of homes in the United States were heated by natural gas. A random sample of206homes found that127were heated by natural gas. Does the evidence support the claim, or has the percentage changed? Use = 0.05and theP-value method.

(a) State the hypotheses and identify theclaim.

H₀ : ____ $______

H₁ : ____ $______

This hypothesis test is a______ -tailed test.

(b) Compute the test value.

(c) Find theP-value.

(d) Make thedecision.

(e) Summarize theresults.

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