Question

Are you likely to purchase an item promoted by a celebrity on a social media site? According to a survey, 26% of social media users have made such a purchase Complete parts (a) through (d) below a Suppose that the survey had a sample size of n = 1000 Construct a 95% confidence n er a estima purchased an item promoted by a celebrity on a social media site. or the po a o opo on of soc al media use s (Type an integer or a decimal. Round to four decimal places as needed.)

Answer 1

Solution :

n = 500

x = 155

$\hat p$ = x / n = 155 / 500 = 0.31

1 -$\hat p$ = 1 - 0.31 = 0.69

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

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

= 1.960* ($\sqrt$((0.310 * 0.690) / 500)

= 0.0405

A 95 % confidence interval for population proportion p is ,

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

0.310 - 0.0405 < p < 0.310 + 0.0405

0.2695 < p < 0.3505

The 95% confidence interval for the population proportion p is : ( 0.2695 , 0.3505)