Question

A 1 7.32. 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. 7.33. A survey wanted to determine what kind of game system was preferred by students. In a

Answer 1

Solution :

Given that,

n = 256

x = 187

Point estimate = sample proportion = $\hat p$ = x / n = 187 / 256 = 0.730

1 - $\hat p$ = 1 - 0.730 = 0.270

At 95% confidence level

$\alpha$ = 1 - 95%

$\alpha$ =1 - 0.95 =0.05

$\alpha$/2 = 0.025

Z$\alpha$/2 = Z_{0.025 = 1.960}

Margin of error = E = Z_{$\alpha$ / 2} * $\sqrt$ (($\hat p$ * (1 - $\hat p$ )) / n)

= 1.96 ($\sqrt$((0.730 * 0.270) / 256)

= 0.054

A 95% confidence interval for population proportion p is ,

$\hat p$ ± E  

= 0.730 ± 0.054

= ( 0.676, 0.784 )