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 400 executives answered Yes, while in a previous year survey, 192 of 400 executives had answered Yes. Provide a 95% confidence interval estimate for the difference between the proportions at the two points in time (to 4 decimal). What is your interpretation of the interval estimate? more executive are predicting an in full-time hobs. The confidence interval shows the difference may be form to .

Explanation / Answer

95 % confidence interval

1 - current survey

2 - previous year

X1 = 230 n1 = 400 , X2 = 192 , n2 = 400

p1^ - p2^ = 230/400 -192/400 = 38/400 =0.0950.

sqrt((230/400*170/400 )/ 400 + (192/400*208/400)/400) = 0.702833551/20 = 0.0351416775

z0.05 = 1.96 *

hence confidence interval is

(0.095 -1.96* 0.0351416775),((0.095+1.96* 0.0351416775))

=(0.02612, 0.163877)

since each point in confidence interval is gretaer than 0 , we conclude that there is increase in the number of full time employee

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