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Student's t test and Z test

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A. A normal distribution has Mu = 40 and standard deviation = 8
Describe the distribution of sample means based on samples of n = 16 selected from this population.
Of all the possible samples of n = 16, what proportion will have sample means greater than 42?
Of all the possible samples of n = 16, what proportion will have sample means less than 39?

B. A statistics instructor would like to know whether it is worthwhile to require students to do weekly homework assignments. For one section of the statistics course, homework is assigned, collected and graded each week. For another section, the same problems are suggested each week, but the students are not required to turn in their homework. At the end of the semester, all students take the same final exam. The grade distribution for the two sections are as follows:

A B C D E
Homework 12 15 17 5 1
No Homework 12 21 28 25 14

Do these data indicate a significant difference between the grade distributions for students with homework verses students with no homework? Test with alpha = .05

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The solution gives the step by step procedure for the calculation of students t test and Z test.

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