Question

A department of education reported that in 2007, 66% of students enrolled in college or a trade school within 12 months of graduating from high school. In 2013, a random sample of 320 individuals who graduated from high school 12 months prior was selected. From this sample, 236 students were found to be enrolled in college or a trade school. Complete parts a through c below. a. Construct a 95% confidence interval to estimate the actual proportion of students enrolled in college or a trade school within 12 months of graduating from high school in 2013. and an upper limit of A 95% confidence interval to estimate the actual proportion has a lower limit of (Round to three decimal places as needed.)

Answer 1

Solution :

Given that,

Point estimate = sample proportion = $\hat p$ = x / n = 236 / 320 = 0.738

1 - $\hat p$ = 1 - 0.738 = 0.262

Z$\alpha$/2 = Z_0.025 = 1.96

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

= 1.96 ($\sqrt$((0.738 * 0.262) / 320)

= 0.048

A 95% confidence interval for population proportion p is ,

$\hat p$ ± E   

= 0.738 ± 0.048

= ( 0.690, 0.786 )

lower limit = 0.690

upper limit = 0.786