Exercise 1047 Algorithmic In June 2001 38 of fund managers s

{Exercise 10.47 (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 110 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).
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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).
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What is the p-value (to 4 decimals)?
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What is your conclusion?
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Solution

Point estimate of the dif =.38-.22= .16

Std dev(diff)=sqrt[(.38)(1-.38)/110 + (.22)(1-.22)/110]=.0608

Test statistic is (.16-0)/.0608=2.63

Reject H0 since test statistic exceeds 1-sided critical value.

(p-value is approx. 1-0.9957= 0.0043)