Question

The President of school wants to know how well Math 1401 students are doing at school. He wants a range for the GPAs. Construct a 95% confidence interval for the population mean GPA.

Adjusted GPA
4
3.5
2.8
2.86
2.31
0
0
2.97
3.21
2.54
3.67
2.17
0
2.91
0
3.61
3.02
2.09
3.5
0
2.25
0
2
4
2.19
3
2.05
2.57
3
3.62
3.31
3.28
3.54
3.88
3.5
0
3.38
2.85
3
3.45
4
2.98
3.51
2.59
2.85
2.37
2.09
2.78
3.35
2.22

1. Sample Mean:10.88
2. Sample Standard Deviation: 3.2679
3. What is the sample size? 50
4. What is the confidence level?   
5. What is the lower bound of the confidence interval?
6. What is the upper bound of the confidence interval?
7. What is the error bound margin?

Answer 1

sample mean, xbar = 10.88
sample standard deviation, s = 3.2679
sample size, n = 50
degrees of freedom, df = n - 1 = 49

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.01

ME = tc * s/sqrt(n)
ME = 2.01 * 3.2679/sqrt(50)
ME = 0.9289

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (10.88 - 2.01 * 3.2679/sqrt(50) , 10.88 + 2.01 * 3.2679/sqrt(50))
CI = (9.9511 , 11.8089)

Lower Bound = 9.9511
upper bound of the confidence interval = 11.8089
MArgin of error = 0.9289