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

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)

Step-by-step explanation:

Given sample size 'n' = 210

The sample proportion 'p' = 51% = 0.51

Confidence intervals are determined by

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

The 92% of z-score value

$Z_{\frac{\alpha }{2} } = Z_{\frac{0.08}{2} } = Z_{0.04} = 1.405$

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

$(0.51 - 1.405 \sqrt{\frac{0.51 (1-0.51 }{210} } , 0.51 +1.405 \sqrt{\frac{0.51 (1-0.51)}{210 } } )$

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)