First semester GPA\'s for a random selection of freshmen at a large university a
ID: 2959967 • Letter: F
Question
First semester GPA's for a random selection of freshmen at a large university are shown below:1.9 +3.2 +2.0 +2.9 +2.7 +3.3 +2.8 +3.0 +3.8 +2.7 +2.0 +1.9 +2.5 +2.7 +2.8+ 3.2 +3.0 +3.8 +3.1 +2.7 +3.5 +3.8 +3.9 +2.7 +2.8 +1.9 +4.0 +2.2 +2.8 +2.1 +2.4 +3.0+ 3.4+ 2.9+ 2.1+ 2.9.
a. What is the best point estimate for the mean GPA of the freshman class.
b. Estimate the true mean GPA of the freshmen class with 99% confidence.
c. Determine the Margin of Error, E for this interval.
d. What happens to the interval if we lower our confidence to 90%? Explain.
"Must see calculator functions." Thanks.
Explanation / Answer
a. What is the best point estimate for the mean GPA of the freshman class.
xbar = mean=(1.9 +3.2 +2.0 +2.9 +2.7 +3.3 +2.8 +3.0 +3.8 +2.7 +2.0 +1.9 +2.5 +2.7 +2.8+ 3.2 +3.0 +3.8 +3.1 +2.7 +3.5 +3.8 +3.9 +2.7 +2.8 +1.9 +4.0 +2.2 +2.8 +2.1 +2.4 +3.0+ 3.4+ 2.9+ 2.1+ 2.9)/36
= 2.844
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b. Estimate the true mean GPA of the freshmen class with 99% confidence.
standard deviatoin= [(1.9-2.844)^2 + (3.2-2.844)^2 + ...+ (2.9-2.844)^2]/(36-1) =0.6
Given a=0.01, Z(0.005)=2.58 (check standard normal table)
So 99% CI is
xbar ± Z*s/n
--> 2.844 ± 2.58*0.6/6
--> ( 2.586, 3.102)
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c. Determine the Margin of Error, E for this interval.
Margin of Error = Z*s/n = 2.58*0.6/6 = 0.258
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d. What happens to the interval if we lower our confidence to 90%? Explain.
Given a=0.1, Z(0.05) = 1.645 (check standard normal table)
So 90% CI is
xbar ± Z*s/n
--> 2.844 ± 1.645*0.6/6
--> ( 2.6795, 3.0085)
So the confidence interval becomes narrow.
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