A 97 confidence interval in inches for the mean height of a

A 97% confidence interval (in inches) for the mean height of a population is (65.4 , 67.0). This result is based on a sample of size 144. Construct the 90% confidence interval.

Solution

a) 97% confidence interval for the mean height is 65.4, 67.0\\

This means x bar lies between mu+2.17 sigma and mu-2.17sigma.

Or we have

5.34 sigma = 67.0-65.4 = 1.6

Or sigm a= 0.2996.

mu - 0.2996(2.17)   = 65.4

So mu = 66.051.

Now based on this value we can calculate for 90% confidence interval.

For 90% Z score is 1.645.

Hence confidence interval at 90% will be

{66.051-1.645(0.2996) , 66.05 +1.645(0.2996) }or

(65.559, 66.544) is the answer.