A fitness course claims that it can improve an individual\'s physical ability. T

Question

A fitness course claims that it can improve an individual's physical ability. To test the effect of a physical fitness course on one's physical ability, the number of sit -ups that a person could do in one minute, both before and after the course, was recorded. Ten individuals are randomly selected to participate in the course. The results are displayed in the following table. Can it be concluded, from the data, that participation in the physical fitness course resulted in significant improvement? Let d- (number of sit ups that can be done after taking the course-number of sit ups that can be done prior to taking the course. Use a s gnificance level of a 0.1 for the test. Assume that the numbers of sit -ups are normally distributed for the population both before and after taking the fitness course. Sit-ups before 21 46 41 30 36 23 52 36 41 25 Sit-ups after 34 58 58 41 53 30 58 45 31 Copy Data Step 2 of s: Find the value of the standard deviation of the paired differences. Round your answer to one decimal place.

Explanation / Answer

Here the difference table is given below

Standard deviation =  sd = 4.8717

standad error of difference in means = 4.8717/sqrt(10) = 1.54

Average difference = dbar =9.8

test statistic = 9.8/4.8717 = 2.0116

Here for alpha = 0.1 and dF = 10 - 1 = 9

tcritical = 1.833

Here

t > tcritical so we would reject the null hypothesis and can conclude that there ispositive difference in number of situps after taking the courese.

Sit-ups before Sit-ups After difference 21 34 13 46 58 12 41 58 17 30 41 11 36 53 17 23 30 7 52 58 6 36 41 5 41 45 4 25 31 6 average 9.8

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