A random sample of 100 students had a mean grade point average (GPA) of 3.2 with a standard deviation of 0.2. The standard error of the sample mean in this case is 0.02. Calculate an approximate 95% confidence interval for the mean GPA for all students.
A) (2.8, 3.6)
B) (3.16, 3.24)
C) (3.18, 3.22)
D) None of the above

Question

Quizplus · Accepted Answer

The 95% confidence interval for the mean is calculated using the formula: mean ± (Z * standard error), where Z is the Z-score for a 95% confidence level (approximately 1.96). Here, the mean is 3.2, and the standard error is 0.02. Thus, the interval is 3.2 ± (1.96 * 0.02) = 3.2 ± 0.0392, which approximates to (3.16, 3.24).

A Random Sample of 100 Students Had a Mean Grade