Question

Wendy wants to estimate the mean number of hours that college students sleep each night. She obtains a simple random sample of 41 college students and finds that the sample mean is 6.7 with a standard deviation of 1.9. Construct a 90% confidence interval to estimate the population mean and interpret your answer in a complete sentence (round numbers to 1 decimal place).

Answer 1

Solution :

Given that,

= 6.7

s = 1.9

n = 41

Degrees of freedom = df = n - 1 = 41 - 1 = 40

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

t /2,df = t0.05,40 =1.684

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

= 1.684 * ( 1.9 / 41)

= 0.5

Margin of error = 0.5

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

- E < < + E

6.7 - 0.5 < < 6.7 + 0.5

6.2 < < 7.2

(6.2, 7.2 )