Question

A 99% confidence interval (in inches) for the mean height of a population is 65.7 < μ < 67.3. This result is based on a sample of size 144. Construct the 95% confidence interval.

a) 66.0 in < μ < 67.0 in.
b) 65.7 in < μ < 67.3 in.
c) 65.6 in < μ < 67.4 in.
d) 65.9 in < μ < 67.1 in.

Answer 1

d) 65.9 in < μ < 67.1 in.

Explanation:

Given that a 99% confidence interval (in inches) for the mean height of a population is 65.7 < μ < 67.3

Mean = average of 65.7 and 67.3 =
`66.5`

i.e. here margin of error =
`67.3-66.5=0.80`

For 99% confidence interval critical value is 2.58

Hence std deviation =
`(0.8)/(2.58)`

For 95% confidence interval critical value is 1.96

Margin of error =
`1.96*(0.8)/(2.58)\\=0.607752`

Hence confidence interval =
`(66.5-0.6, 66.5+0.6)\\= (65.9, 67.1)`

d) 65.9 in < μ < 67.1 in. is right