Question

Would you favor spending more federal tax money on the arts? Of a random sample of n = 93 politically conservative voters, 1 = 17 responded yes. Another random sample of n2 = 78 politically moderate voters showed that r2 - 22 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 a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. OMO:P<P; H: P1 = P2 OHO: P = Pz; HP#P2 OHO: P = Pz: H: P > P2 O Ho: P2 = Px; HP, <P2 (b) What sampling distribution will you use? What assumptions are you making? The Student's t. We assume the population distributions are approximately normal. 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. The number of trials is sufficiently large. What is the value of the sample test statistic? (Test the difference p - P. Do not use rounded values. Round your final answer to two decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.)

Answer 1

get the los be d.o. Ho: Pi= P2 Hi P < P₂ The Standard normal we ass The no. of tralls are sustellently large. let B 0.18 0.28 pooled proportion, p- ni bit na mit P- 22417 tz nith 93470 0.22 9-1-p-0.7 test statistic Ps, Z = bib Pal6+) = 0.18 - 0.18-0.28 Z Jo. 22(0.78 ) [q3 11/13) Z: -1.57 p-value = 0.0582 - -246 1 2 3 At the x = 0.05 we fall to refect the Null hypothesis and conclude the data are not Statistically significant

e) 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.