Question: Test scores in stat 1342 course are assumed to be normally distributed. A sample of 21 students was selected for a study of variability in the test scores. The sample summaries obtained from the sample are shown below.

[sample mean] = 63.7 and [sample standard deviation] =5.

1. Estimate the population variance with the \(99 \%\) confidence. Round the confidence limits to the 2 ^nd decimal place.
   
2. At the \(1 \%\) significance level, do we have sufficient evidence that the population variance exceeded 15 ?
3. At the \(1 \%\) significance level, do we have sufficient evidence that the population variance was below 50 ?

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