At a particular academically challenging high school, the average GPA of a high school senior is known to be normally distributed. After a sample of 20 seniors is taken, the average GPA is found to be 2.71 and the variance is determined to be 0.25. Find a 90% confidence interval for the population mean GPA.
A) [2.5167, 2.9033]
B) [2.5261, 2.8961]
C) [2.5615, 2.8585]
D) [2.6358, 2.7842]

Question

Quizplus · Accepted Answer

Given the sample size (n = 20), the sample mean ($\bar{x}$ = 2.71), and the sample variance (s^2 = 0.25), we can calculate the 90% confidence interval for the population mean using the formula for the confidence interval of the mean when the population variance is unknown and the sample size is small (n < 30). This involves using the t-distribution. The correct choice, [2.5167, 2.9033], accounts for the variability in the sample and the level of confidence desired, using the appropriate degrees of freedom (n-1 = 19) and the standard error of the mean.

At a Particular Academically Challenging High School, the Average GPA