Question

A statistics professor at a large university hypothesizes that students who take statistics in the morning typically do better than those who take it in the afternoon. He takes a random sample of 36 students who took a morning class and, independently, another random sample of 36 students who took an afternoon class. He finds that the morning group scored an average of 74 with a standard deviation of 8, while the evening group scored an average of 68 with a standard deviation of 10. The population standard deviation of scores is unknown but is assumed to be equal for morning and evening classes. Let µ1 and µ2 represent the population mean final exam scores of statistics’ courses offered in the morning and the afternoon, respectively. At the 1% significance level, does the evidence support the professor’s claim?

Answer 1

The answer is 2.381

Explanation:

From the information given from the question, we solve for the evidence support of the professor's claim

Given that:

x₁ = 74,

n₁ = 36

s₁ = 8

x₂ = 68

n₂ = 36

s₂ = 10

The hypotheses are:

Critical value = t₃₆+₃₆-₂,₀.₀₁ = t₇₀,₀.₀₁

so,

t₃₆+₃₆-₂,₀.₀₁ = t₇₀,₀.₀ = 2.381

That is, - 2.381 to 2.381

Therefore, we support professor's claim