10.3 1) Would you favor spending more federal tax money on the arts? Of a random
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Question
10.3
1) Would you favor spending more federal tax money on the arts? Of a random sample of n1 = 91 politically conservative voters, r1 = 20 responded yes. Another random sample of n2 = 77politically moderate voters showed that r2 = 24 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 ? = 0.05.
(a) What is the level of significance?
(b) What is the value of the sample test statistic? (Test the difference p1 ? p2. 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.)
2) Do you prefer paintings in which the people are fully clothed? This question was asked by a professional survey group on behalf of a national arts organization. A random sample of n1 = 58 people who are conservative voters showed that r1 = 45 said yes. Another random sample of n2 = 64 people who are liberal voters showed that r2 = 38 said yes. Does this indicate that the population proportion of conservative voters who prefer art with fully clothed people is higher? Use ? = 0.05
(a) What is the level of significance?
(b) What is the value of the sample test statistic? (Test the difference p1 ? p2. 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.)
3) Would you favor spending more federal tax money on the arts? Of a random sample of n1 = 218 women, r1 = 61 responded yes. Another random sample of n2 = 195 men showed that r2 = 49 responded yes. Does this information indicate a difference (either way) between the population proportion of women and the population proportion of men who favor spending more federal tax dollars on the arts? Use ? = 0.01. Solve the problem using both the traditional method and the P-value method. (Test the difference p1 ? p2. Round the test statistic and critical value to two decimal places. Round the P-value to four decimal places.)
test statistic critical value ± P-valueExplanation / Answer
Solution1:
Ho:p1=p2
H1 :p1 not p2
(a) What is the level of significance
alpha=0.05
(b) What is the value of the sample test statistic?
z=p1^-p2^/sqrtp1^(1-p^)/n1+p2^(1-p2^)/n2
p1^=20/91=0.2197802
p2^=24/77=0.3116883
Z=(0.2197802-0.3116883)/sqrt(0.2197802*(1-0.2197802)/91+0.3116883*(1-0.3116883)/77)
Z=-1.35
Solutionc:
to get p value:
p=0.0885
p>0.05
Fail to reject Ho.
No sufficinet evidence to support the claim
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