SOLUTION: exam grades a statistics professor is used to having a variance in his class grades of no more than 100. he feels that his current group of students is different, and so he exami

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Question 1188257: exam grades
a statistics professor is used to having a variance in his class grades of no more than 100. he feels that his current group of students is different, and so he examines a random sample of midterm grades as shown. at α = 0.05, can it be concluded that the variance in grades exceeds 100?
92.3 89.4 76.9 65.2 49.1 96.7 69.5 72.8 67.5 52.8 88.5 79.2 72.9 68.7 75.8
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the sample variance is 183.78.

the standard deviation of the sample is square root of that = 13.56.
the sample size is 15.

the standard error = 13.56 / sqrt(15) = 3.5.

the t-score is equal to (x - m) / s

x is the mean of the sample.
m is the assumed mean
s is the standard error.

formula becomes:

t = (183.78 - 100) / 3.5 = 23.94.

the one tailed critical t-score with 14 degrees of freedom = 1.76.

the test t-score is way beyond this.
it is reasonable to conclude that the variation in the test scores from the sample is definitely higher than 100 and that the difference is not due to normal variations in the mean of different samples of the same size.