A random sample of 51 observations was selected from a normally distributed population. The sample mean was = 88.6, and the sample variance was s2 = 38.2. Does the sample show sufficient reason to conclude that the population standard deviation is not equal to 8 at the 0.05 level of significance? Use the p-value method.
A researcher wishes to compare two different groups of students with respect to their mean time to complete a particular task. The time required is determined for each group. The data summary is given below. Test the claim at = 0.05, that there is no variance. Give the critical region, test statistic value, and conclusion for the F test.
The number of sit-ups that a person can do in one minute, both before and after a physical fitness course was recorded. The data is shown below for 10 randomly selected participants. Is there sufficient evidence to conclude that a significant amount of improvement took place? Assume variable is normally distributed. Test using  = 0.01.
Before 30 23 25 29 27 25 30 45 34 26
After 31 27 25 35 34 35 32 52 50 43
The solution answers the question(s) below.