Question

Strategic business planning is required for the successful transfer of control between generations in family owned companies. A survey of 17 family firms whose annual turnover exceeded one million dollars found that 28% had no strategic business plan. Assuming that simple random sampling was employed, estimate with 95% confidence the proportion of family-owned companies operating without strategic business plans. What is the upper limit and lower limit of this estimate (for four decimal places)?

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = 0.28

1 - = 1 - 0.28 = 0.72

Z/2 = Z0.025 = 1.96

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.96 (((0.28 * 0.72) / 17 )

= 0.2134

A 95% confidence interval for population proportion p is ,

± E  

= 0.28  ± 0.2134

= ( 0.0666, 0.4934 )

lower limit = 0.0666

upper limit = 0.4934