Mathematics, 06.03.2020 23:51 shardonnay2160

Some researchers are interested in the GPA difference between freshmen and sophomores. The distributionsof GPAs in both groups are approximately normal. From previous school records, we know that themean and standard deviation for freshmen are 3.5 and 0.5, respectively. Similarly, the mean and standarddeviation for sophomores are 3.2 and 0.8, respectively. Independent random samples of 40 students areto be selected from both years (for a total of 80 students).

a. If the sample mean GPA is to be calculated for both groups and we calculate the diﬀerence between freshmen and sophomores, what is the expected value for the diﬀerence in sample means?
b. If the sample mean GPA is to be calculated for both groups and we calculate the diﬀerence between freshmen and sophomores, what is the standard deviation of the sampling distribution of the diﬀerence in sample means?
c. What is the probability that the average GPA in freshmen is higher than the average GPA in the sample of sophomores?

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