Would you rather spend more federal taxes on art? Of a random sample of \(n_{1} = 86\) politically conservative voters, \(r_{1} = 18\) responded yes. Another random sample of \(n_{2} = 85\) politically moderate voters showed that \(r_{2} = 21\) responded yes. Does this information indicate that the population proportion of conservative voters inclined to spend more federal tax money on funding the arts is less than the proportion of moderate voters so inclined? Use \(\alpha = 0.05.\)
(a) State the null and alternate hypotheses.
\(H_0:p_{1} = p_{2}, H_{1}:p_{1} > p_2\)

\(H_0:p_{1} = p_{2}, H_{1}:p_{1} < p_2\)

\(H_0:p_{1} = p_{2}, H_{1}:p_{1} \neq p_2\)

\(H_{0}:p_{1} < p_{2}, H_{1}:p_{1} = p_{2}\)
(b) What sampling distribution will you use? What assumptions are you making?
The Student's t. The number of trials is sufficiently large.
The standard normal. The number of trials is sufficiently large.The standard normal. We assume the population distributions are approximately normal.
The Student's t. We assume the population distributions are approximately normal.
(c)What is the value of the sample test statistic? (Test the difference \(p_{1} - p_{2}\). Do not use rounded values. Round your final answer to two decimal places.)
(d) Find (or estimate) the P-value. (Round your answer to four decimal places.)
(e) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level alpha?
At the \(\alpha = 0.05\) level, we reject the null hypothesis and conclude the data are statistically significant.
At the \(\alpha = 0.05\) level, we fail to reject the null hypothesis and conclude the data are statistically significant.
At the \(\alpha = 0.05\) level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
At the \(\alpha = 0.05\) level, we reject the null hypothesis and conclude the data are not statistically significant.
(f) Interpret your conclusion in the context of the application.
Reject the null hypothesis, there is sufficient evidence that the proportion of conservative voters favoring more tax dollars for the arts is less than the proportion of moderate voters.
Fail to reject the null hypothesis, there is sufficient evidence that the proportion of conservative voters favoring more tax dollars for the arts is less than the proportion of moderate voters.
Fail to reject the null hypothesis, there is insufficient evidence that the proportion of conservative voters favoring more tax dollars for the arts is less than the proportion of moderate voters.
Reject the null hypothesis, there is insufficient evidence that the proportion of conservative voters favoring more tax dollars for the arts is less than the proportion of moderate voters.