The US Department of Energy reported that 51\% of homes were heated by natural gas. A random sample of 305 homes in Oregon found that 132 were heated by natural gas. Test the claim that the proportion of homes in Oregon that were heated by natural gas is different than what was reported. Use a 5\% significance level. Give answers to at least 4 decimal places.
- What are the correct hypotheses? (Select the correct symbols and use decimal values, not percentages.)
$H_0$: [ ? ] p [ ? ] 0.51
$H_A$: [ ? ] p [ ? ] 0.51
- Based on the hypotheses, find the following:
Test Statistic = [ ? ]
p-value = [ ? ]
- Based on the above, we choose to [Reject / Fail to reject] the null hypothesis.
- State the correct summary conclusion.
$H_A$: [ ? ] p [ ? ] 0.51
p-value = [ ? ]