Would you favor spending more federal tax money on the arts? This question was a
ID: 3269065 • Letter: W
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Would you favor spending more federal tax money on the arts? This question was asked by a research group on behalf of The National Institute (Reference: Painting by Numbers, J. Wypijewski, University of California Press). Of a random sample of n1 = 93 politically conservative voters, r1 = 21 responded yes. Another random sample of n2 = 83 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 = 0.05. What is the level of significance? Level of significance State the null and alternate hypotheses. Check Requirements. What sampling distribution will you use? What assumptions are you making? O Standard normal, since the number of trials are sufficiently large. O Student's t, since the number of trials are not sufficiently large. Compute the sample test statistic. (Round your answer to two decimal places.) Sample test statistic =Explanation / Answer
It is given, alpha=0.05. Therefore, level of significance is 0.05.
Assume p1 and p2 denote population proportion of conservative voters and population proportion of moderate voters inclined to spend more on federal tax for arts. The researcher wants to know whether p1<p2. Thus the null hypothesis which is the hypothesis of no difference (there is no difference between p1 and p2) and alternative hypothesis are as follows:
H0:p1=p2 versus H1:p1<p2
Options 1, 2 and 3 are wrong as they donot follow the notations correctly.
Distributions, for large number of trials (n1=93, n2=83), the distribution to be used is normal. t distribution is not suitable correct option.
Sample test statistic.
The samples are independent, r1=21, n1-r1=93-21=72, r2=22, n2-r2=83-22=61 are all greater than 5.
Compute pooled sample proportion.
Phatp=(r1+r2)/(n1+n2)=(21+22)/(93+83)=0.2443
Z=(p1hat-p2hat)/sqrt[phatp(1-phatp)]sqrt[1/n1+1/n2], where, p1hat and p2hat are sample proportion.
=(21/93-22/83)/sqrt[0.2443(1-0.2443)]sqrt[1/93+1/83]
=-0.61
Using technology, p value is 0.545.
The alternative hypothesis is left tailed. Therefore, shade area to the left of -|sample statistic| (note the sign of test statistic is negative). Option 2 and 3 are automatically discarded.
The p value (0.545) is greater than alpha(0.05), therefore, fail to reject null hypothesis. Option 1 is naturally wrong.
Since, one fails to reject null hypothesis, there is naturally insufficient sample evidence to support the alternative hypothesis. Thus among options 1 and 4, option 1 is correct as it correctly interpret the conclusion.
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