Question

The average exam score for students enrolled in statistics classes at Indiana University Northwest is 80 and grades are normally distributed. A professor decides to select a random sample of 25 students from his CJ statistics class to see how CJ students compare to the student body in terms of exam performance. The average exam score of this sample is 78 with a variance equal to 100. Are the stats exam scores of the students in the CJ class significantly different when compared to the average university student at IUN?

a. Reach a statistical conclusion

b. Interpret your results

c. What would be your statistical conclusion and interpretation if the size of the selected sample would be 100?

2. Using the information provided at Q1, calculate the 95% confidence interval of the mean stats exam scores for the population of CJ students enrolled at IUN. [sample size = 25]

a. Interpret the 95%CI

b. Test the hypothesis that the CJ students’ population mean at stats exam is 80. Do you reject or fail to reject the null hypothesis? Justify your conclusion.

Answer 1

1)Given the sample size and sample mean , sample standard deviation .

The   two sided confidence interval for mean based on the sample data is

The hypotheses are

The 95% CI for mean is

Since , we accept the null hypothesis.

a) The conclusion is that "the stats exam scores of the students in the CJ class are not significantly different when compared to the average university student at IUN".

b) WE are 95% confident that the mean lies in the interval .

When , The 95% CI for mean is

Since , we reject the null hypothesis.

a) The conclusion is that "the stats exam scores of the students in the CJ class are significantly different when compared to the average university student at IUN".

b) WE are 95% confident that the mean lies in the interval .

2)Answer in part (1).