Question

A math professor has been teaching graduate statistics for several. His records show that the overall mean for final exam scores is 82 with a standard deviation of 10. The professor believes that last year’s class scores are greater than his previous classes. He decides to conduct a test on the 25 students enrolled in one of his statistics class. Construct and interpret 95% and 99% confidence intervals. Assume that the professor increased his sample size to 50 when he analyzed another section of his statistics classes. If he performed the same tests how would the conclusions differ?

Answer 1

given that

mean = 82

standard deviation = 10

sample size n = 25

95% Confidence interval (z critical = 1.96, using z table)

CI=

99% Confidence interval (z critical = 2.58, using z table)

CI=

We know that the confidence interval width and the sample size varies inversely with each other. So, when we increase the sample size, then the confidence interval width will gets reduced.