Question

Based on a random sample of

1140

​adults, the mean amount of sleep per night is

8.56

hours. Assuming the population standard deviation for amount of sleep per night is

1.3

​hours, construct and interpret a

90​%

confidence interval for the mean amount of sleep per night.

A

9090​%

confidence interval is

​(nothing​,nothing​).

​(Round to two decimal places as​ needed.)

Interpret the confidence interval.

Answer 1

Confidence interval is given by the formula,

$\mu$$\pm$ z* $\sigma / \sqrt{n}$

Here, $\mu$ = 8.56hours

$\sigma$ = 1.3 hours

n = 1140

z* for 90% confidence level is 1.645

Confidence interval CI = 8.56 $\pm$ 1.645x$1.3/\sqrt{1140}$

= 8.56 $\pm$ 0.0633

= (8.4967, 8.6233)

We can be 90% confident that the the population mean lies in the interval (8.4967, 8.6233)