In 2016, the mean number of runs scored by both teams in a Major League Baseball

Question

In 2016, the mean number of runs scored by both teams in a Major League Baseball game was 9.22. Collecting data on 24 games in 2017 resulted in a mean of 8.29 and a standard deviation of 4.15.
a) Assuming the number of runs is normal, test to see if the mean number of runs has changed. Test the appropriate hypothesis at Alpha = 0.10.
b) If the true mean number of runs in 2017 is 8.29, what is the probability that we conclude there has not been a change in the mean at Alpha = 0.10. Would you be comfortable accepting the null hypothesis from part (a)? Explain.

Explanation / Answer

the mean number of runs scored by both teams in a Major League Baseball game was 9.22

Collecting data on 24 games in 2017 resulted in a mean of 8.29 and a standard deviation of 4.15.

a. t = (8.29-9.22)/(4.15/sqrt(24)) = -1.0978

For df = 24-1=23 and t = -1.098 we have critical value as t = -1.714

Since, t = -1.0978 is more than -1.714 we will fail to reject null hypothesis ( Ho : Mu = 9.22)

and conclude that MEan number of runs has NOT changed

b) If the true mean is 8.29 then the t value is = (8.29-8.29)/(4.15/sqrt(24)) = 0, p value = .50 which is much more than .10

Again, we will not reject null hypothesis and conclude the same ( As part a) BUT this time we have a t value which is farther from the critical value / In other words the we have lesser evidence than in part a to reject null hypothesis.

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