Californiaand New York lead the list of average teachers' salaries. The California yearly average is $ 64,421 while teachers in New York make an average annual salary of $62,332. Random samples of 50 teachers from each state yielded the following.

California (sample 1)New York (sample 2)Sample mean64,15062,410Population standard deviation8,2317,716

A.At = 0.01, is there a difference in means of the salaries?

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

1.

H₀:₁= ₂

H₁:₁< ₂(claim)

2.

H₀:₁=₂

H₁:₁> ₂(claim)

3.

H₀:₁=₂

H₁:_{1 2}(claim)

b) Find the critical value (s).

1. CV=1.65

2. CV= 2.33

3. CV= 2.58

c) Compute the test value:

1. TV= -1.05

2. TV=1.09

3. TV= 1.18

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 the 99% confidence interval for the difference between the two means.

1. -2376.5<₁- ₂<5856.5

2. -1977.6<₁- ₂<5457.6

3. -892.6<₁- ₂<4372.6