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David Anderson has been working as a lecturer at Michigan StateUniversity for the last three years. He teaches two large sectionsof introductory accounting every semester. While he uses the samelecture notes in both sections, his students in the first sectionoutperform those in the second section. He believes that studentsin the first section not only tend to get higher scores, they alsotend to have lower variability in scores. David decides to carryout a formal test to validate his hunch regarding the difference inaverage scores. In a random sample of 20 students in the firstsection, he computes a mean and a standard deviation of 85.2 and25.9, respectively. In the second section, a random sample of 21students results in a mean of 85.0 and a standard deviation of1.18.

Sample 1 consists of students in the first section and Sample 2represents students in the second section.

a.	Construct the null and the alternative hypotheses to testDavid’s hunch.
	H0: μ1 −μ2 = 0; HA:μ1 − μ2 ≠ 0 H0: μ1 −μ2 ≥ 0; HA:μ1 − μ2 < 0 H0: μ1 −μ2 ≤ 0; HA:μ1 − μ2 > 0

b-1.	Calculate the value of the test statistic.(Round all intermediate calculations to atleast 4 decimal places and final answer to 2 decimalplaces.)

  Test statistic

 Â

b-2.	What assumption regarding the population variances is used toconduct the test?
	Known population standard deviations. Unknown population standard deviations that are equal Unknown population standard deviations that are not equal

c.	Implement the test at α = 0.10 using the criticalvalue approach.
	Reject H0; there is evidence that scoresare higher in the first section. Reject H0; there is no evidence that scoresare higher in the first section. Do not reject H0; there is evidence thatscores are higher in the first section. Do not reject H0; there is no evidence thatscores are higher in the first section.