Question

Homework: HW 9.1 9.2 9.3 Score: 0 of 1 pt 17 of 40 (25 complete) 9.1.39 A television sports commentator wants to estimate the proportion of citizens who "Yollow professional football. Complete parts (a) theough (c). (a) What sample size should be obtained if he wants to be within 4 percentage points with 95% confidence if he uses an estimale of 48% oblained from a pol? (obo eu oug o dn punoy) azs odues ou

Answer 1

Solution:

Given that,

$\hat p$$\hatp$ = 0.48

1 - $\hat p$ = 1 - 0.48 = 0.52

margin of error = E = 4% = 0.04

At 95% confidence level the z is ,

$\alpha$ = 1 - 95% = 1 - 0.95 = 0.05

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

Z_$\alpha$/2 = Z_0.025 = 1.960

Sample size = n = ((Z_{$\alpha$ / 2}) / E)² * $\hat p$ * (1 - $\hat p$ )

= (1.960 / 0.04)² * 0.48 * 0.52

= 599.2896

= 599

n = sample size = 599