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, 191 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 decimals). Use z-table.

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Answer 1

Solution :

Given that,

n₁ = 400

x₁ = 230

₁ = x₁ / n₁ = 0.575

n₂ =400

x₂ = 191

₂ = x₂ / n₂ = 0.478

1) Point estimate of difference between two proportions

= ₁ -  ₂

= 0.575 - 0.478

= 0.097

2)

Our aim is to construct 95% confidence interval.

c = 0.95

= 1- c = 1- 0.95 = 0.05

  /2 = 0.05 2 = 0.025

= 1.96 (use z table)

Margin of error =   *

=  

=

= 0.0689

3) Required interval is

Point estimate   Margin of error

0.097   0.0689

(0.097 - 0.0689, 0.097 +  0.0689)

(0.0281 , 0.1659 )