Question

Question 13 of 18 (1 point) Attempt 1 of Unlimited 7.3 Section Exercise 15-18 Use the given data to construct a 98% confidence interval for the population proportion p. x = 47, n=71 Round the answer to at least three decimal places. The confidence interval is

Answer 1

Solution :

n = 71

x = 47

$\hat p$ = x / n = 47/ 71 = 0.662

1 -$\hat p$ = 1 - 0.662 = 0.338

At 98% confidence level the z is ,

$\alpha$ = 1 - 90% = 1 - 0.90 = 0.02

$\alpha$ / 2 = 0.02 / 2 = 0.01

Z_$\alpha$/2 = Z_0.01 = 2.326

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

= 2.326 * ($\sqrt$((0.662 * 0.338) / 71)

= 0.130

A 98 % confidence interval for population proportion p is ,

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

0.662 - 0.130 < p 0.662 + 0.130

0.531 < p < 0.792