Two groups of students aregiven a problem-solving test, and the results are compared.Assume that both variables are normally distributed.

Mathematics majorsComputer science majorsSample mean = 83.6Sample mean = 79.2Population standard deviation = 4.3Population standard deviation = 3.8sample size = 36sample size = 36

A.Test the claim that Mathematics studentshave different resultsfrom computer science students. Use =0.1.

a) State the hypotheses and identify the claim with the correct hypothesis.

1.

H₀:_{M CS}

H₁:_M< _CS(claim)

2.

H₀:_M= _CS

H₁:_{M CS}(claim)

3.

H₀:_{M CS}

H₁:_M> _CS(claim)

b) Find the critical value (s).

1. CV=1.65

2. CV=-2.33

3. CV= 1.28

c) Compute the test value:

1. 3.30

2. -1.67

3. 4.6

d) Make the decision.

1. Reject the null hypothesis.

2.Do not reject the null hypothesis.

e) Summarize the results.

1. There is enough evidence to support the claim.

2.There is not enough evidence to support the claim.

B.Find the95%confidence intervalof the true difference in the means.

1.[-3.56;0.36]

2.[1.93;6.87]

3.[2.53;6.27]