Question

Connie Rodrigues, the Dean of Students at Midstate College, is wondering about grade distributions at the school. She has heard grumblings that the GPAs in the Business School are about 0.25 lower than those in the College of Arts and Sciences. A quick random sampling produced the following GPAs

Business: 2.86 2.77 3.18 2.80 3.14 2.87 3.19 3.24 2.91 3.00 2.83
Sciences: 3.35 3.32 3.36 3.63 3.41 3.37 3.45 3.43 3.44 3.17 3.26 3.18 3.41

Do these data indicate that there is a factual basis for the grumblings?

Answer 1

To determine if there is a factual basis for the grumblings about the difference in GPAs between the Business School and the College of Arts and Sciences at Midstate College, we can compare the grade distributions of the two schools.

Step-by-step explanation:

To determine if there is a factual basis for the grumblings about the difference in GPAs between the Business School and the College of Arts and Sciences at Midstate College, we can compare the grade distributions of the two schools.

1. Calculate the mean GPA for each school by adding all the GPAs together and dividing by the number of GPAs in each sample. The mean GPA for the Business School is 2.95, and the mean GPA for the College of Arts and Sciences is 3.36.
2. Calculate the standard deviation for each school to measure the spread of the data. The standard deviation for the Business School is 0.16, and the standard deviation for the College of Arts and Sciences is 0.11.
3. Compare the mean GPAs and standard deviations to determine if there is a significant difference between the two schools. Since the means and standard deviations are different, there may be a factual basis for the grumblings about the lower GPAs in the Business School compared to the College of Arts and Sciences.