Question

This is a re-post to question 2. The question was answered but the response was all jumbled up. Can i please have specific answers to questions asked here.

For a better read, I have them in bold fonts below. Please this is urgent. Thanks.

Question 2. Senior executives were asked of their opinion about the future economic outlook. One question inquired, ‘if there will be increase in number of full time employees at their organization in next 12 months’. In the current survey, 220 of 400 executives answered ‘Yes’. While in the 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?

1. The computed error is ____________________________________________________
2. The computed confidence interval is ________________________________________
3. Your interpretation of the interval estimate is ___________________________________

Answer 1

a)

p1 = 220/400 = 0.55
p2 = 192/400 = 0.48

The computed error is = sqrt(p1*(1-p1)/n1+ p2*(1-p2)/n2)

= sqrt(0.55 *(1-0.55) /400 + 0.48 *(1-0.48)/400)
= 0.0353

Margin of error = z *SE
= 1.96 * 0.0353
= 0.0691

b)

z value at 95% =1.96

CI = (p1 - p2) +/- z *SE
= ( 0.55 - 0.48) +/- 1.96 * 0.0353
= (0.0009 , 0.1391 )

The computed confidence interval is (0.0009 , 0.1391)

c)

We are 95% Confident that the proportions at the two points in time is between (0.0009 , 0.1391 )