The proportion of students at a college who have GPA higher than 3.5 is 19%. a.
ID: 3156405 • Letter: T
Question
The proportion of students at a college who have GPA higher than 3.5 is 19%. a. You take repeated random samples of size 25 from that college and find the proportion of student who have GPA higher than 3.5 for each sample. What is the mean and the standard error of the sampling distribution of the sample proportions? b. You take repeated random samples of size 50 from that college and find the proportion of student who have GPA higher than 3.5 for each sample. What is the mean and the standard error of the sampling distribution of the sample proportions? c. Compare the results of parts a and b, and sketch the sampling distributions.
Explanation / Answer
a.The mean is same as the population mean 0.19.
The variance is: sq rt of p(1-p)/n
=sq rt of 0.19(1-0.19)/25
=0.078
b.The mean is same as the population mean 0.19.
The variance is: sq rt of p(1-p)/n
=sq rt of 0.19(1-0.19)/50
=0.055
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