The grade point averages for 10 randomly selected high school students are liste
ID: 3434633 • Letter: T
Question
The grade point averages for 10 randomly selected high school students are listed below. Assume the grade point averages are normally distributed.
Find a 98% confidence interval for the true mean.
(a) What is the average GPA? (Round the answer to two decimal places. Hint: you may want to enter the data to TI graphing calculator for answers of mean and standard deviation.)
(b) What is the standard deviation for the distribution of GPA?
(c) What is the margin of error for the estimate?
(d) What is the lower limit of the confidence interval?
(e) What is the upper limit of the confidence interval?
GPA 2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8Explanation / Answer
(a) What is the average GPA? (Round the answer to two decimal places. Hint: you may want to enter the data to TI graphing calculator for answers of mean and standard deviation.)
average = 2.54
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(b) What is the standard deviation for the distribution of GPA?
standard deviation = 1.109755
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(c) What is the margin of error for the estimate?
margin of error =s/vn
=1.109755/sqrt(10)
=0.3509353
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(d) What is the lower limit of the confidence interval?
The degree of freedom =n-1=10-1=9
Given a=0.98=0.02, t(0.01, df=9) =2.82 (from student t table)
xbar - t*s/vn = 2.54 -2.82*0.3509353 = 1.550362
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(e) What is the upper limit of the confidence interval?
xbar + t*s/vn = 2.54 +2.82*0.3509353 =3.529638
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