A Businessweek/Harris survey asked senior executives at large corporations their

Question

A Businessweek/Harris survey asked senior executives at large corporations their opinions about the economic outlook for the future. One question was, "Do you think that there will be an increase in the number of full-time employees at your company over the next 12 months?" In the current survey, 230 of 500 executives answered Yes, while in a previous year survey, 193 of 500 executives had answered Yes.

Provide a 95% confidence interval estimate for the difference between the proportions at the two points in time (to 4 decimals). Use z-table.

What is your interpretation of the interval estimate? more executives are predicting in full-time jobs. The confidence interval shows the difference may be from to .

Explanation / Answer

p1^=230/500=0.46

p2^=193/500=0.386

z crit for 95%=1.96

p1^-p2^)+-zcrit sqrt(p1^(1-p1^)/n1+p2^(1-p2^)/n2)

(0.46-0.386)+-1.96 sqrt(0.46)(1-0.46)/500+0.386(1-0.386)500)

0.074+-0.06107

lower limit=0.074-0.06107=0.01293

upper limit=0.074+0.06107=0.13507

we are 95% confident tha t the difference in proportions lies in between 0.01293 and 0.13507

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