A) The internal Revenue Service believes that the number of business executives

Question

A) The internal Revenue Service believes that the number of business executives who default on their taxes is larger than the proportion of 'blue collar" workers. Out of 150 business executives, 24 default on their taxes. For a sample of 75 'blue collar' workers has only 8 that default on their taxes. Test the hypothesis that the proportion of business executives who default of their taxes is larger than the proportion of 'blue-collar' workers at a a=.01. (-Round all of the following to 3 decimal places p^1, q^1, p^2 and q^2, p^ and q^. -Round Test statistic to 2 decimal places) B) Find 99% Confidence Interval for the difference of the two proportions.

Explanation / Answer

(A) H0 : proportion of business executives who default of their taxes is same as the proportion of 'blue-collar' workers. Ha : proportion of business executives who default of their taxes is larger than the proportion of 'blue-collar' workers .

p^1 = 24/150 = 0.16 and p^1 = 8/75 = 0.1067

q^1 = 0.84 and p^1 = 0.8933

Pooled estimate p = (24 + 8)/ (150 + 75) = 0.1422

standard error of the pooled estimate se0 = sqrt [ p * (1-p) * (1/n1 + 1/n2)] = sqrt [0.1422 * 0.8578 * (1/150 + 1/75)] = 0.0494

Test Statistic

Z = (p^1 - p^2 )/ SE0 = (0.16 - 0.1067)/ 0.0494 = 1.08

(B) 99% Confidence interval = (p^1 -p^2 ) +- Z95% se0

= (0.16 - 0.1067) +- 1.96 * 0.0494

= 0.0533 +-0.0968

= (-0.0435, 0.1501)

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