Question

A. Tina the best point of estimate of the population of portion p. B. Identify the value of the margin of error E. E= round to four decimal places as needed. C. Construct the confidence interval. _<p<_round to three decimal places. D. Write a statement that correctly interprets the confidence interval.

Answer 1

Solution :

Given that,

n = 2488

x = 1191

A) Point estimate = sample proportion = $\hat p$ = x / n = 1191 / 2488 = 0.479

1 - $\hat p$ = 1 - 0.479 = 0.521

At 99% confidence level

$\alpha$ = 1 - 99%

$\alpha$ =1 - 0.99 =0.01

$\alpha$ /2 = 0.005

Z $\alpha$ /2 = Z0.005 = 2.576

B) Margin of error = E = Z $\alpha$ / 2 * $\sqrt$ (( $\hat p$ * (1 - $\hat p$ )) / n)

= 2.576 ( $\sqrt$ ((0.479 * 0.521) / 2488 )

= 0.0258

C) A 99% confidence interval for population proportion p is ,

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

0.479 - 0.0258 < p < 0.479 + 0.0258

( 0.453 < p < 0.505 )

D) We are 99% confident that the true proportion from an online group involved with ears between 0.453 and 0.505.