Hello everyone,

I am having difficulty understanding hypothesis testing.

I know the 5 steps of completing the test but cannot seem to calculate the correct numbers. For example, here is an exercise my professor provided in class.

A friend makes a claim that municipalities in Pennsylvania start law enforcement officers at $42,000 a year. You decide that they are wrong- you think that Pennsylvania starting law enforcement officers have a different average salary than what your friend says. To test this, you gather salay information for 15 municipalities and obtain the following statistics:

Mean Salary is 39,780

Standard Deviation is 2,500

Perform a hypothesis test to determine if your sample is truly different than the population mean. Use alpha level. 05

What I have so far is my null hypothesis is = 42000

My alternative hypothesis is less than 42000.

Does this make sense? If not please advise

Second, I know the alpha level is .05 meaning the critical value is 2.145 and I know this because this test is 2 tailed and it is a t table I would use because there are 15 municipalities and any number under 50 is using a T table. From here I am lost. Where in the formula do I plug in the critical value?

Thank you for helping !