Question

QUESTION 8 Suppose you sather data from 21 college seniors abut how many contacts they've had with the WSU Police Department during their college experience. You find that seniors have had an average of 4.1 contacts with the police at WSU with a standard deviation of 2.3. Using this information, construct a 95% confidence interval for the mean number of contacts WSU seniors have had with the WSU Police Department during their time at WSU. Be sure to interpret your results TTT Arial 3 (12pt) TEE-5102 B IX Words: Path:p

Please be sure to interpret your results. Also, please type out the answer as oppose to uploading an image with the correct answer. Thank you!

Answer 1

Solution :

Given that,

$\bar x$ = 4.1

s = 2.3

n = 21

Degrees of freedom = df = n - 1 = 21 - 1 = 20

At 95% confidence level the t is ,

$\alpha$  = 1 - 95% = 1 - 0.95 = 0.05

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

t_{$\alpha$ /2,df} = t_0.025,20 =2.086

Margin of error = E = t_{$\alpha$/2,df} * (s /$\sqrt$n)

= 2.086 * (2.3 / $\sqrt$ 21)

= 1.05

Margin of error = 1.05

The 99% confidence interval estimate of the population mean is,

$\bar x$ - E < $\mu$ < $\bar x$ + E

4.1 - 1.05 < $\mu$ < 4.1 + 1.05

3.05 < $\mu$ < 5.15

(3.05, 5.15 )