Question

Suppose you want to know the average amount of sleep you get per night. You record your elapsed sleep time over 35 nights. The mean is 7.1 and standard deviation is 2.3. Find a 95% confidence interval for your mean number of hours of sleep per night. Report the answer accurate to four decimal places

< μμ <

Answer 1

Solution :

degrees of freedom = n - 1 = 35 - 1 = 34

t/2,df = t0.025,34 = 2.032

Margin of error = E = t/2,df * (s /n)

= 2.032 * ( 2.3 / 35)

Margin of error = E = 0.7900

The 95% confidence interval estimate of the population mean is,

- E < < + E

7.1 - 0.7900 < < 7.1 + 0.7900

6.3100 < < 7.8900