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. Data set (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. What is the sample size?
2. What is the confidence level?

What is the lower bound of the confidence interval?

What is the upper bound of the confidence interval?

What is the error bound margin?

Answer 1

Answer Date: 10/11/2019 The sample size is 50. The confidence level is 95%. The error bound margin is, First, compute standard deviation, t-critical value then find margin of error. The standard deviation of GPA is, First, compute sample mean then find sample standard deviation of GPA. The sample mean is, _4 +3.50 +.....+3.35 +2.22 50 = 2.5754

The sample standard deviation of GPA is, (x; – ) Vn-1 (4-2.5754)+(3.50 -2.5754)+.....+(3.50 -2.5754)2 + (2.22 - 2.5754) 50-1 =1.1835 Thet critical value is, The two-tailed test, Look in the column headed a = 0.05 and the row headed in the t distribution table by using degree of freedom is, d.f.=n-1 = 50 - 1 = 49 The t critical value is 2.010.

– 2.010 ( 1.1859 = 0.3363 The error bound margin is 0.3363 . A 95% confidence interval for the population mean GPA is, 95%C.I. = + E = 2.5754 +0.3363 = 2.2391 to 2.9117 A 95% confidence interval for the population mean GPA is between 2.2391 and 2.9117. 2.2391 and the upper bound of the The lower bound of the confidence interval is confidence interval is 2.9117