College admissions administrators at a university are reevaluating their entrance requirements.They believe that the mean GPA for graduating high school seniors has increased dramatically over the last decade.They randomly sample 85 records of graduating seniors from 10 years ago (sample 1) and find an average GPA of 2.68.An independent random sample of 80 current graduating seniors yields an average GPA of 2.94.If the population variance of high school GPAs is 0.2601, does it appear that there was an increase in mean GPA over the last decade? Select the correct p-value and decision below.Use α = 0.01.Also, state H₀.
A) p-value = 0.0005; fail to reject H₀; The null hypothesis is that GPA remained the same.
B) p-value = 0.0010; fail to reject H₀; The null hypothesis is that GPA remained the same.
C) p-value = 0.0005; reject H₀; The null hypothesis is that GPA remained the same.
D) p-value = 0.0010; reject H₀; The null hypothesis is that GPA changed over time.

Question

Quizplus · Accepted Answer

We are conducting a two-sample t-test to compare the means of two independent samples with unknown and unequal variances. The null hypothesis is that there is no difference in mean GPAs between the two samples, or in other words, the mean GPA has remained the same over time. We use a significance level of α = 0.01.

The test statistic is calculated as:

t = (2.94 - 2.68) / sqrt((0.2601/80) + (0.2601/85)) = 6.17

Using software or a t-table, the p-value is found to be very small, p-value = 0.0005. This is smaller than our significance level, so we reject the null hypothesis.

Therefore, we can conclude that there is evidence to suggest that the mean GPA for graduating high school seniors has increased over the last decade.

College Admissions Administrators at a University Are Reevaluating Their Entrance