Textbook Problem

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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, 220 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. What is your interpretation of the interval estimate?

To determine

Find and interpret the 95% confidence interval estimate for the difference between the proportions at two points of time.

Explanation of Solution

Calculation:

In current year survey among a sample of 400 executives, 220 executives feel that there will be an increase in the number of full-time employees in their company over the next 12 months and in previous year survey among a sample of 400 executives, 220 executives feel that there will be an increase in the number of full-time employees in their company over the next 12 months.

Confidence interval:

The interval estimate of the difference between two population proportions is,

$\text{Confidence interval}=\left({\overline{p}}_1-{\overline{p}}_2\right)\pm z_{\frac{\alpha }{2}}\times \sqrt{\frac{{\overline{p}}_1\left(1-{\overline{p}}_1\right)}{n_1}+\frac{{\overline{p}}_2\left(1-{\overline{p}}_2\right)}{n_2}}$

$\alpha$ is the level of significance