Joel, I have not checked all your calculations, but the process you used looks good. I note that this is a problem where you are given a lot of raw data. Which technology did you use? I ask because problems where you have to manually enter a lot of raw data often lead to mistakes just in keying the data in.
Here is another MSL problem where you really have a lot to key in because there are 30 sample values each with 5 digits to enter.
I worked it in Excel and would like to point out two other things:
- One key is to recognize you are given the population standard deviation, sigma, so you should use the z-test.
- You must recognize the claim and state it both in words and math symbols. If you do that correctly, then doing the math become easier as does writing the conclusion.
Here, because we have a right-tail test, we must subtract the values we get from the tables or basic Excel functions from 1. Failing to recognize this results in the many, many mistakes I see in student quizzes with a P-value that is the wrong tail.
And if you know which hypothesis the claim is, writing the conclusion becomes a lot easier.
I would also note that in the image, I show how to get Excel to use the basic logic of hypothesis tests to “make” the Reject or Fail to Reject decision automatically using Excel functions AND and IF. On the calculators on my website, I take it one more step and get Excel to write the conclusion too. This is not difficult to do if you want to create your own Excel calculators which you can then use on quizzes and exams.