The US Department of Energy reported that 49% of homes in the USA were heated by natural gas. A random sample of 313 homes in Oregon found that 171 were heated by natural gas. Test the claim that proportion of homes in Oregon that were heated by natural gas is different from the US reported proportion. Use a 10% significance level. Give answers accurate to at least 3 decimal places.

What are the correct hypotheses? (Select the correct symbols and use decimal values not percentages.)

H₀: Select an answer σ s μ σ² s² p̂ p x̄ ? ≤ ≠ > = < ≥

H₁: Select an answer σ s² p p̂ s x̄ μ σ² ? < ≥ = > ≠ ≤  

Based on the hypotheses, find the following:

Test Statistic =

p-value =

Based on the above we choose to Select an answer Accept the null hypothesis Accept the alternative hypotheis Fail to reject the null hypothesis Reject the null hypothesis

The correct summary would be: Select an answer There is enough evidence to reject the claim There is not enough evidence to reject the claim There is not enough evidence to support the claim There is enough evidence to support the claim that the percent of homes in Oregon heated by natural gas is different than 49%.