Question

Furniture Land surveyed 690 consumers and found that 418 were enthusiastic about a new home decor it plans to show in its store in High Point Construct the 95% confidence interval for the population proportion (Round the final answers to 3 decimal places.) Confidence interval for the population proportion is and

Answer 1

Solution :

Given that,

n = 690

x = 418

Point estimate = sample proportion = $\hat p$ = x / n = 418/690 = 0.6058

1 - $\hat p$ = 1-0.6058 = 0.3942

At 95% confidence level

$\alpha$ = 1-0.95% =1-0.95 =0.05

$\alpha$/2 =0.05/ 2= 0.025

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

Z_$\alpha$/2 = 1.960

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

= 1.960 * ($\sqrt$(0.6058*(0.3942) /690 )

= 0.036

A 95% confidence interval for population proportion p is ,

$\hat p$ - E < p < $\hat p$ + E

0.6058-0.036 < p < 0.6058+0.036

0.569 < p < 0.642

( 0.569 ,0.642 )

confidence interval for the population proportion is 0.569 and 0.642 .