1. ## Hypothesis testing statistics

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.

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 !

2. ## Re: Hypothesis testing statistics

Hey Asuk1234.

For a null hypothesis you are looking at a probability that one hypothesis is true given the data. The second applies equally.

Usually what you do is you get a range of values for the hypothesis and get a test statistic that is used to get the probability that the hypothesis is true given the data that is used to get the test statistic in the first place.

Hint - Can you figure out the test statistic and probabilities for both hypotheses?