Fortyfive members of a bowling league sign up for a program

Forty-five members of a bowling league sign up for a program that claims to improve bowling scores. The participants bowl a set of five games before the program begins and a set of five games again at the end to measure their improvement. The mean number of points improved (over the set of five games) was x= 18. Assume the standard deviation is sigma = 59 and let 4u be the population mean number of points improved for the set of five games. To determine whether the program is effective, a test is made of the hypotheses H0: mu= 0 versus H1: mu > 0. Do you reject H0 at the a = 0.01 level? Select one: A.No B. Yes C. There is not enough information to draw a conclusion.

Solution

H0: mu=0

Ha: mu >0

Right tailed test for sample mean

x bar =18, sigma = 59

xbar - mu = 18

std error = 59/rt 5 = 26.385

t statistic = 18/std error = 0.6822

Alpha = 0.01

df =5-1 = 4

p value = 0.266285

As p > 0.01, accept null hypothesis.

Hence answer is

No, we do not reject null hypothesis.