The US Department of Energy reported that 47% of homes were heated by natural gas. A random sample of320 homes in Oregon found that 157 were heated by natural gas. Test the claim that proportion of homesin Oregon that were heated by natural gas is different than what was reported. Use a 1 % significancelevel. Give answer to at least 4 decimal places.a. What are the correct hypotheses? (Select the correct symbols and use decimal values not percentages.)Ho: Select an answerH₁: Select an answerBased on the hypotheses, compute the following:b. Test Statistic =? 0c. p-value=d. Based on the above we choose to Select an answerCthat the proportion ofe. The correct summary would be: Select an answerhomes in Oregon that were heated by natural gas is different than what the DOE reported value of 47%.Question Help: Video Message instructorSubmit Question Jump to Answer

The sample size, i.e., the sampled number of homes, n=320.The number of sampled houses, that are heated by natural gas, x=157.The hypothesized proportion of homes, that are heated by natural gas, p0=47% (or 0.47).Part (a)Considering p as the true proportion of homes, that are heated by natural gas, it is set up as follows:H0:p=0.47; the proportion of homes that are heated by natural gas is hypothesized to be indifferent to 47%.H1:p≠0.47; the proportion of homes that are heated by natural gas is hypothesized to be not indifferent to 47%.Part (b)The sample proportion of homes that are heated by natural gas, i..e,p^=xn=157320≈0.490625The test statistic is:z=p^−p0p0(1−p0)n=0.490625−0.470.47×(1−0.47)320=0.739234254≈0.7392Part (c)The p-value (tao-tailed) for the z-score of 0.7392 is obtained using the excel function "2∗(1−NORM.S.DIST(z,cumulative))" as follows:The p-value is 0.4598Part (d)The decision rule is: "reject H0, p-value≤α".For significance level, α=1%=0.01, p-value (=0.4598)>α. Thus H0 is failed to be rejected.Part (e)The proportion of homes that are heated by natural gas is concluded to be indifferent to 47%.(a) H0:p=0.47; H1:p≠0.47;(b) The test statistic is 0.7392.(c) The p-value is 0.4598.(d) Based on the above we chose to accept (or retain) the null hypothesis.(e) There is insufficient evidence to conclude that the proportion of homes in Oregon that were heated by natural gas is different than what the DOE reported value of 47%.