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 400 executives answered Yes, while in a previous year survey, 199 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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What is your interpretation of the interval estimate?

Select0%5%10.25%14%Item 3 more executives are predicting Selectan increasea decreaseItem 4 in full-time jobs. The confidence interval shows the difference may be from Select3%5%7%14%Item 5 to Select0%5%7%17%Item 6 .

Answer 1

first sample size,     n1=   400
number of successes, sample 1 =     x1=   240
proportion success of sample 1 , p̂1=   x1/n1=   0.6
      
second sample size,     n2 =    400
number of successes, sample 2 =     x2 =    199
proportion success of sample 1 , p̂ 2=   x2/n2 =    0.4975
      
difference in sample proportions,    p̂1 - p̂2 =     0.1025 or 10.25%

Std error , SE =    SQRT(p̂1 * (1 - p̂1)/n1 + p̂2 * (1-p̂2)/n2) =     0.0350
Z critical value =   Z α/2 =    1.9600
      
margin of error , E =   Z*SE =    0.0686
      
confidence interval is       
lower limit =    (p̂1 - p̂2) - E =    0.0339 or 3%
upper limit =   (p̂1 - p̂2) + E = 0.1711 or 17%

What is your interpretation of the interval estimate?

10.25%more executives are predicting an increase in full-time jobs. The confidence interval shows the difference may be from 3% to 17%