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, 240 of 500 executives answered Yes, while in a previous year survey, 194 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. to What is your interpretation of the interval estimate? Select more executives are predicting Select ▼ n fu time Jobs. The confidence interval shows the difference may be rom Select to Select

Answer 1

0.00concider current survey,

240 of 500 employee are answered yes,

so, sample proportion P1=240/500=0.48

now, Concider previous survey,

194 of 500 executive had answered yes,

so, sample proportion P2=194/500.=0.388

now, setting up hypothesis,

null hypotesis Ho: P1=P2

alternative hypothesis H1: p1>p2.

Test statistic;

$Z=(p1-p2)/root(P1(1-p1)/n1)+p2*(1-P2)/n2)$

z=3.204

so, p value for z score=0.000678, which is less than 0.05

so we reject the null hypothesis.

now, solving for confidence interval:-

C.I.=(0.0308,0.1532)

so our confidence interval is  0.0308 to 0.1532.

so, we conclude that

Yes more executive are predicting increse in full time jobs

so, the confidence interval show that difference may be varry from 0.0308 to 0.1532