{Exercise 11.33 (Algorithmic)} In June 2001, 38% of fund managers surveyed belie
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Question
{Exercise 11.33 (Algorithmic)} In June 2001, 38% of fund managers surveyed believed that the core inflation rate would be higher in one year. One month later a similar survey revealed that 22% of fund managers expected the core inflation rate to be higher in one year (Global Research Highlights, Merrill Lynch, July 20, 2001). Assume that the sample size was 140 in both the June and July surveys. Develop a point estimate of the difference between the June proportion (population 1) and the July proportion (population 2) of fund managers who felt the core inflation rate would be higher in one year (to 2 decimals). Develop hypotheses such that rejection of the null hypothesis allows us to conclude that inflation expectations diminished between June and July. H0: p1 - p2 Ha: p1 - p2 Conduct a test of the hypotheses in part (b) using = .01. Compute the value of the test statistic (to 2 decimals). What is the p-value (to 4 decimals)? What is your conclusion?
Explanation / Answer
Ho : p1 -p2 = 0
Ha: p1 -p2 > 0
E(p1^ -p2^) = p1 -p2
p1^ = 0.38 , p2^ = 0.22
p1^ -p2^ = 0.16
n1 =n2 = 140
p = 0.5 *(0.38 + 0.22) = 0.30 { as n1 = n2}
TS = (p1^ - p2^)/sqrt(pq*(1/n1 + 1/n2))
=(0.38 - 0.22)/(sqrt(0.3*0.7*(2/140))
=2.92118697
p-value = P(Z> 2.92118697) = 0.0017
since p-value < 0.01
we reject the null hypothesis
and conclude that there is significant evidence that inflation expectations diminished between June and July.
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