tion 11 3 pts The Brookings Institute recently published a survey of 1500 college students regarding...

Question

Question

math Statistics-And-Probability

Answer 1

Answer #1

Solution :

Given,

n = 1500 ....... Sample size

x = 765 .......no. of successes in the sample

Let $\hat p$ denotes the sample proportion.

$\therefore$ $\hat p$ = x/n = 765 / 1500 = 0.51

Our aim is to construct 90% confidence interval.

$\therefore$ c = 0.90

$\therefore$ $\alpha$ = 1- c = 1- 0.90 = 0.10

$\therefore$ $\alpha$ /2 = 0.10 $\slash$ 2 = 0.05 and 1- $\alpha$ /2 = 0.950

$\therefore$ $2012$ = 1.645 (use z table)

Now , the margin of error is given by

E = $2012$ * $Vp(1-P)/n$

= 1.645 * $\sqrt{}$ [ 0.51 *(1 - 0.51)/1500]

= 0.021

Now the confidence interval is given by

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

( 0.51 - 0.021) $< p <$ ( 0.51 + 0.021 )

0.489 $< p <$ 0.531

Required 90% Confidence Interval is ( 0.49 , 0.53 )

Answer 2