Question

Suppose a 95% confidence interval, based upon a sample of size 25, for the mean number of hours of sleep that college students get per night was 5 to 8 hours. How many students should be surveyed in order to cut the width of the interval down from 3 hours to 1.5 hours?

Answer 1

100 students should be surveyed in order to cut the width of the interval down from 3 hours to 1.5 hours

Explanation:

Given that a 95% confidence interval, based upon a sample of size 25, for the mean number of hours of sleep that college students get per night was 5 to 8 hours.

Confidence interval = (5,8)

This implies that mean = 6.5 and margin of error = 1.5

i.e.
`1.5 =1.96*(s)/(√(25) )`

If the interval width to be cut into half then the

New confidence interval = (5.75, 7.25)

Margin of error = 0.75

`0.75=1.96*(s)/(√(n) )`

This is possible only when new n= 100

Hence sample size should be increased to 100

100 students should be surveyed in order to cut the width of the interval down from 3 hours to 1.5 hours