Suppose that student acceptance data at a four-year university shows that, in a

Question

Suppose that student acceptance data at a four-year university shows that, in a given year, the high school GPA of freshmen at acceptance to the university is symmetrically distributed with mean 3.83 and standard deviation 0.097. A random sample of 75 different freshmen from the same year is selected, and their average GPA is found to be 3.70, Suppose you took numerous repeated samples of size 75. From the Rule for Sample Means, you _________ expect the frequency curve of means from the various samples to be approximately bell-shaped (normal)in this sample the average GPA is _________ than you would expect for a sample of size 75. In 68% of samples of 75 freshmen from the same year, the sample mean should fall within the interval _______

Explanation / Answer

Rule of sample means IF:1.The population of measurements of interest is bell-shaped, OR2.A large sample (at least 30) is taken.THEN:If numerous samples of the same size are taken and the sample mean is computed every time, the resulting histogram will:1.be roughly bell-shaped2.have mean equal to the true population mean3.have standard deviation estimated bysample standard deviationsample size sd=sd/sqrt(n)

based on this first blank will be should, second would be lower and for third we will do calculation as below

P(z1<x<z2)=0.68, using z table we get z1=-0.994=x1bar- 3.70/0.097/sqrt(75), so x1bar=3.689

and x2bar=3.711

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