The US Department of Energy reported that 51.7% of homes were heated by natural gas. A random sample of 221 homes in Kentucky found that 115 were heated by natural gas. Does the evidence support the claim for Kentucky at the α = 0.05 level in Kentucky? Are the results applicable across the country? Why?

$H_0:p=0.517;H_a:p\ne 0.517$

$p-value=0.9203$

In one to two complete sentences, explain what the p-value means for this problem. If the null hypothesis is true (the proportion is 0.517), then there is a 0.9203 probability that the sample (estimated) proportion is 0.520 or more.

Conclusion: At the 5% significance level, there is not enough evidence to conclude that the proportion of homes in Kentucky that are heated by natural gas is 0.517.

However, we cannot generalize this result to the entire nation. First, the sample’s population is only the state of Kentucky. Second, it is reasonable to assume that homes in the extreme north and south will have extreme high usage and low usage, respectively. We would need to expand our sample base to include these possibilities if we wanted to generalize this claim to the entire nation.