Question

Before adding a new kind of burger to its menu, a fast food restaurant first conducts a market survey to see if customers will like it. Out of the 256 customers surveyed, 187 said that they would buy the burger. Construct and interpret a 95% confidence interval to estimate the proportion of customers that would buy the new burger if it were sold to the general public.

Answer 1

Sample proportion = 187 / 256 = 0.730

95% confidence interval for p is

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

0.730 - 1.96 * sqrt [ 0.730 ( 1 - 0.730) / 256 ] < p < 0.730 + 1.96 * sqrt [ 0.730 ( 1 - 0.730) / 256 ]

0.676 < p < 0.784

95% CI is ( 0.676 , 0.784 )

Interpretation - We are 95% confident that the proportion of customers that would buy the new burger

if it were sold to the general public is between 0.676 and 0.784