Question

Question 2 (8 points) 25 Pittsburgh residents were asked how much sleep they get per night. The mean was 7.2 hours and the standard deviation was .78 hours. Construct and interpret 90% confidence interval for the true mean number of hours of sleep for Pittsburgh residents. BIU Format

Answer 1

Solution :

Given that,

Point estimate = sample mean = $\bar x$ = 7.5

sample standard deviation = s = .78

sample size = n = 25

Degrees of freedom = df = n - 1 = 25 - 1 = 24

At 90% confidence level the t is ,

$\alpha$ = 1 - 90% = 1 - 0.90 = 0.10

$\alpha$ / 2 = 0.10 / 2 = 0.05

t_{$\alpha$ /2,df} = t_0.05,24 = 1.711

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

= 1.711 * (.78 / $\sqrt$ 25)

= 0.3

The 90% confidence interval estimate of the population mean is,

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

7.2 - 0.3 < $\mu$ < 7.2 + 0.3

6.9 < $\mu$ < 7.5

(6.9 , 7.5)