Question

According to Franchise Business review, over 50% of all food franchises earn a profit of less than $50,000 a year. In a sample of 142 casual dining restaurants, 81 earned a profit of less than $50,000 last year.

What is the point estimate of the proportion of casual dining restaurants that earned a profit of less than $50,000 last year? (round to two decimal places) Answer

Develop a 95% confidence interval for the proportion of casual dining restaurants that earned a profit of less than $50,000 last year. (round to two decimal places) [Answer , Answer]

Answer 1

Sample proportion = 81 / 142 = 0.57

Point estimate of the proportion = = 0.57

95% confidence interval for proportion p is

- Z/2 * sqrt [ ( 1 - ) / n) ] < p < + Z/2 * sqrt [ ( 1 - ) / n) ]

0.57 - 1.96 * sqrt( 0.57 * 0.43 / 142 ) < p < 0.57 + 1.96 * sqrt( 0.57 * 0.43 / 142 )

0.49 < p < 0.65

95% confidence interval is ( 0.49 , 0.65 )