# Suppose the mean height in inches of all 9th grade students at one

high school is estimated. The population standard deviation is 5

inches. The heights of 8 randomly selected students are 66, 75, 71, 68, 67, 74, 74 and 66.

Answer the following:

Margin of error at 90% confidence level =

90% confidence interval =

Margin of error at 90% confidence level =2.9067

90% confidence interval = (67.21,73.03)

First, we determine the mean of the sample.

$xˉ=n∑x =866+75+71+68+67+74++74+66 =$ 70.125

second, we determine the margin of error

$Given,xˉ=70.125n=8σ=5n s =1.767step 1 calculate,Z_{2α}=1−α=0.9,then,α=1−0.9=0.1,2α ==0.05,1−0.05=0.95Π(0.95)z_{2α}=1.645Step 2 margin of error :z_{2α}∗n s =1.645∗1.767=2.9067 $

third we determine the confidence interval

$Given,xˉ=70.125n=8s=5n s =1.767step 1 calculate,Z_{2α}=1−α=0.9,then,α=1−0.9=0.1,2α ==0.05,1−0.05=0.95Π(0.95)z_{2α}=1.645Step 2 the confidence interval can be calculated as:(xˉ−z_{2α}∗n s ,xˉ+z_{2α}∗n s )Putting the given values we get(70.125−1.645∗1.767,70.125+1.645∗1.767)Hence, the required confidence interval is:(67.21,73.03) $