Question

Coopers & Lybrand surveyed 210 chief executives of fast-growing small companies. Only 51% of these executives had a management succession plan in place. A spokesperson for Cooper & Lybrand said that many companies do not worry about management succession unless it is an immediate problem. However, the unexpected exit of a corporate leader can disrupt and unfocus a company for long enough to cause it to lose its momentum. Use the data given to compute a 92% confidence interval to estimate the proportion of all fast-growing small companies that have a management succession plan.

Answer 1

92% Of confidence intervals to estimate the proportion of all fast-growing small companies that have a management succession plan.

(0.46154 , 0.558)

Explanation:

Given sample size 'n' = 210

The sample proportion 'p' = 51% = 0.51

Confidence intervals are determined by

`(p^(-) - z_(\alpha ) \sqrt{(p^(-) (1-p^(-) )/(n) } , p^(-) +Z_(\alpha ) \sqrt{(p^(-) (1-p^(-) ))/(n ) } )`

The 92% of z-score value

`Z_{(\alpha )/(2) } = Z_{(0.08)/(2) } = Z_(0.04) = 1.405`

92% Of confidence intervals to estimate the proportion of all fast-growing small companies that have a management succession plan.

`(0.51 - 1.405 \sqrt{(0.51 (1-0.51 )/(210) } , 0.51 +1.405 \sqrt{(0.51 (1-0.51))/(210 ) } )`

on calculation , we get

(0.51-0.048 , 0.51 + 0.048)

(0.46154 , 0.558)

Final answer:-

92% Of confidence intervals to estimate the proportion of all fast-growing small companies that have a management succession plan.

(0.46154 , 0.558)