Hypothesis Test(Stat)

[IdRatherSleep]

"The mean length of a work week for the population of workers was reported to be 39.2 hours. Suppose that we would like to take a current sample of workers to see whether the mean length of a work week has changed from the previously reported 39.2 hours."
1.- State the hypothesis that will help us determine whether a change occurred in the mean length of a work week?
2.-Suppose a current sample of 112 workers provided a sample mean of 38.5 hours. Use a population standard deviation of 4.8 hours. What is the p value?

I have no idea how to do this problem, I would really appreciate if someone could at least answer the first question. Thanks and I hope you can help me.

 

[galactus]

For the first part, the claim is "the mean is different from 39.2".

Can you state the null and alternative hypotheses from this statement?.

You can use:

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

to find your p-value.

 

[IdRatherSleep]

What I don't get if this is an upper tail test or two tail test? Would the hypothesis be:
Null: Mean equal or less than 39.2
Alternative: Mean greater than 39.2

 

[galactus]

I'm thinking two-tail because they're asking for any change in the mean, which implies "not equal to".

\(\displaystyle \L\\H_{0}:{\mu}=39.2\)

\(\displaystyle \L\\H_{0}:{\mu}\neq{39.2}\)