Question

The US Department of Energy reported that 46% of homes were heated by natural gas. A random sample of 338 homes in Oregon found that 131 were heated by natural gas. Test the claim that proportion of homes in Oregon that were heated by natural gas is different than what was reported Use a 10% significance level. Give answer to at least 4 decimal places. What are the correct hypotheses? (Select the correct symbols and use decimal values not percentages) Based on the hypotheses, find the following Test Statistic p-value- Based on the above we choose to Select an answer The correct summary would be: Accept the afternative hypotheis Select an answer that the proportion of homes in Oregon that were heated by natural gas is different than what 1 Fail to reject the null hypothesis Reject the null hypothesis Accept the null hypothesis License

Answer 1

$\small H_0:p=0.46$

$\small H_1:p\neq0.46$

Test Statistic = $\small Z=\frac{\hat{p}-p}{\sqrt{{p}(1-p)/n}}$ = -2.6716

p-value = 0.003774135*2 = 0.0075

As p-value < 0.10, we reject the null hypothesis and the correct summary would be There enough evidence to reject the claim .