Inferential Statistics

I have six similar problems and need help getting started. I think I can follow a formula for figuring out the others if I get help with the first.
Problem #1. The Rocky Mountain district sales manager of JCM, Inc., a college book publishing company, claims that each of his sales reps make 40 calls on professors per week. Several reps said that this estimate is too low. To research the claim, a random sample of 28 reps revealed that the mean number of calls made last week was 42. The standard deviation of the sample was computed to be 2.1 calls. At the .05 level of significance, can we conclude that more than 40 calls are made on the average in a week? Thanks, Bob

I will step through this one so you can have a template for the others...Okey-doke?.

The thought is that 40 is too low, so we have:

\(\displaystyle H_{0}:{\mu}\leq 40\)
\(\displaystyle H_{a}:{\mu}>40 \;\ \text{claim}\)

It is a right tailed test.

Since n<30, we can use a t-distribution.

\(\displaystyle z=\frac{(x-{\mu})\sqrt{n}}{\sigma}\)

\(\displaystyle t=\frac{(42-40)\sqrt{28}}{2.1}=5.04\)

There are 28-1=27 degrees of freedom. So, looking in the t-table, we find t=1.703 is the critical value.

The rejection region is \(\displaystyle t\geq 1.703\)

Since t is in the rejection region, we decide to reject the null hypothesis.

There is enough evidence at the .05 level to support the claim that the mean number of calls is greater than 40.

That means the publishers claim that their sales reps make an average of 40 calls per week is too low.

Thanks so much