Would you favor spending more federal tax money on the arts? Ofa random sample of n1 = 95 politicallyconservative voters, r1 = 16 responded yes.Another random sample of n2 = 77 politicallymoderate voters showed that r2 = 20 respondedyes. Does this information indicate that the population proportionof conservative voters inclined to spend more federal tax money onfunding the arts is less than the proportion of moderate voters soinclined? Use α = 0.05.
(a) What is the level of significance?
State the null and alternate hypotheses.
H0: p1 =p2; H1:p1 >p2H0:p1 < p2;H1: p1 =p2    H0:p1 = p2;H1: p1 <p2H0:p1 = p2;H1: p1 ≠p2
(b) What sampling distribution will you use? What assumptions areyou making?
The standard normal. The number of trials is sufficientlylarge.The Student's t. We assume the populationdistributions are approximately normal.    TheStudent's t. The number of trials is sufficientlylarge.The standard normal. We assume the population distributionsare approximately normal.
What is the value of the sample test statistic? (Test thedifference p1 − p2. Do notuse rounded values. Round your final answer to two decimalplaces.)
(c) Find (or estimate) the P-value. (Round your answer tofour decimal places.)
(d)Sketch the sampling distribution and show the area correspondingto the P-value.
(e) Based on your answers in parts (a) to (c), will you reject orfail to reject the null hypothesis? Are the data statisticallysignificant at level α?
At the α = 0.05 level, we reject the null hypothesisand conclude the data are statistically significant.At theα = 0.05 level, we fail to reject the null hypothesis andconclude the data are statisticallysignificant.    At the α = 0.05 level,we fail to reject the null hypothesis and conclude the data are notstatistically significant.At the α = 0.05 level, we rejectthe null hypothesis and conclude the data are not statisticallysignificant.
(f) Interpret your conclusion in the context of theapplication.
Fail to reject the null hypothesis, there is insufficientevidence that the proportion of conservative voters favoring moretax dollars for the arts is less than the proportion of moderatevoters.Fail to reject the null hypothesis, there is sufficientevidence that the proportion of conservative voters favoring moretax dollars for the arts is less than the proportion of moderatevoters.    Reject the null hypothesis, there isinsufficient evidence that the proportion of conservative votersfavoring more tax dollars for the arts is less than the proportionof moderate voters.Reject the null hypothesis, there is sufficientevidence that the proportion of conservative voters favoring moretax dollars for the arts is less than the proportion of moderatevoters.
