A newspaper is doing a story on comparing two different county court systems. Of

Question

A newspaper is doing a story on comparing two different county court systems. Of interest is the proportion of jurors called up for jury duty in a given week who are disqualified for service. For a recent week, in Lincoln county n1 = 100 jurors were called of which X1 = 25 were disqualified while in Jefferson county n2 = 150 jurors were called of which X2 = 45 were disqualified.

Assume that a binomial distribution is appropriate as the probability model for both counties.

Compute separate two sided 95% confidence intervals for each sample using both the normal approximation method and the exact methods. Discuss which method you would give more credence and why.

Conduct a hypothesis test at 5% significance of whether the population proportions are identical or not. Compare the test results to a comparison of the two confidence intervals in the previous part and discuss if the conclusions should be identical or not. Also compare hypothesis test result to a 95% confidence interval on the difference in proportions. What does the CI tell you that the test does not?

If the newspaper decided that if the difference between the rates of disqualified jurors is 10% or more (or |p1 – p2| > .1) it would be significant enough to warrant a follow up article investigating what factors might be causing the difference, what sample sizes would be adequate? Assume they would plan to test the hypothesis of equality at the 1% significance level and want to achieve a power of 95%.  

MiniTab needs to be used for all parts and the outputs need to be shown.

Explanation / Answer

minitab output

Test and CI for Two Proportions

Sample X N Sample p
1 25 100 0.250000
2 45 150 0.300000

Difference = p (1) - p (2)
Estimate for difference: -0.05
95% CI for difference: (-0.162164, 0.0621641)
Test for difference = 0 (vs not = 0): Z = -0.86 P-Value = 0.388

Fisher's exact test: P-Value = 0.472

here p-value = 0.38 > 0.05 so that we can claim that two proportions are equal at 95% confidence

also
95% CI for difference: (-0.162164, 0.0621641)

that interval contains zero and so that zero is in the interval claims that two proportions are same

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