Suppose your statistics instructor gave six examinations during the semester. Yo
ID: 3059858 • Letter: S
Question
Suppose your statistics instructor gave six examinations during the semester. You received the following grades (percent correct): 79, 73, 88, 90, 95, and 77. Instead of averaging the six scores, the instructor indicated he would randomly select two grades and compute the final percent correct based on the two percents.
a.How many different samples, without replacement, of two test grades are possible?
Compute the mean of the sample means and compare it to the population mean. (Round your answers to 3 decimal places.)
The population mean is
The mean of the sample means is
Compute the mean of the sample means and compare it to the population mean. (Round your answers to 3 decimal places.)
The population mean is
The mean of the sample means is
Explanation / Answer
Total grades = 6
a) Number of different smaples possible = 6C2 = 6! / (2! * (6-2!) = 15
Population mean = (79 + 73 + 88 + 90 + 95 + 77) / 6 = 83.667
Sample Mean
(79 , 73) 76
(79 , 88) 83.5
(79 , 90) 84.5
(79 , 95) 87
(79 , 77) 78
(73 , 88) 80.5
(73 , 90) 81.5
(73 , 95) 84
(73 , 77) 75
(88 , 90) 89
(88 , 95) 91.5
(88 , 77) 82.5
(90 , 95) 92.5
(90 , 77) 83.5
(95 , 77) 86
The mean of the sample means = (76 + 83.5 + 84.5 + 87 + 78 + 80.5 + 81.5 + 84 + 75 + 89 + 91.5 + 82.5 + 92.5 + 83.5 + 86) / 15 = 83.667
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