Question

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 =

Answer & Explanation
Verified Solved by verified expert

Margin of error at 90% confidence level =2.9067

90% confidence interval = (67.21,73.03)

Step-by-step explanation

First, we determine the mean of the sample.

xˉ=nx=866+75+71+68+67+74++74+66= 70.125

 second, we determine the margin of error

Given,xˉ=70.125n=8σ=5ns=1.767step 1 calculate,Z2α=1α=0.9,then,α=10.9=0.1,2α==0.05,10.05=0.95Π(0.95)z2α=1.645Step 2 margin of error :z2αns=1.6451.767=2.9067

 third we determine the confidence interval

Given,xˉ=70.125n=8s=5ns=1.767step 1 calculate,Z2α=1α=0.9,then,α=10.9=0.1,2α==0.05,10.05=0.95Π(0.95)z2α=1.645Step 2 the confidence interval can be calculated as:(xˉz2αns,xˉ+z2αns)Putting the given values we get(70.1251.6451.767,70.125+1.6451.767)Hence, the required confidence interval is:(67.21,73.03)