This is a video on a Hypothesis Test for a Mean.

The question states: Students are supposed to spend an average of 2 hours studying for

every hour of lecture. Juan thinks students spend an average less than 2 hours. He surveys

36 students who averaged 1.8 hours with a standard deviation of 1.3 hours. What can be

concluded with

alpha=0.1? Let’s first state the null hypothesis. The null hypothesis is

that the average or the population mean is 2 hours, because that’s what Juan is trying to

prove is incorrect. In symbols, H0 is write down the cast of characters. The average

for the sample was 1.8 hours, so xBar=1.8. The standard deviation for this

sample of 36 students was 1.3 hours. So the sample standard deviation s is 1.3. There

were 36 students surveyed. That’s the sample size. n=36. Now we’re ready to use

our calculator. Here’s the calculator. I want to do a T-Test because I don’t know the

population standard deviation. So I go to STAT and then TESTS. Then I scroll down 1 to

T-Test and hit ENTER. I am given statistics, so I do want Stats, so I scroll down. mu0, that’s

the null hypothesis value, mu=2, so statistic: t=-0.92 about. The P-Value is 0.18.

Now let’s go back to the PowerPoint. The test statistic t was about equal to -0.92 and

the P-Value was about equal to 0.18. I am interested in comparing the P-Value with the

level of significance alpha=0.1. Notice that 0.18>0.10, so the P-Value is greater

than the level of significance. I can say that if it were true that mu was equal to

2 then there would be an 18% chance of conducting a study of the same sample size

and coming up with a sample mean at or below 1.8. And 18% is a pretty big percent chance.

That means I fail to reject the null hypothesis. Let’s state the conclusion. We can

say that Juan fails to reject the null hypothesis. The data is inconclusive. There is

insufficient evidence to support the claim that students on average spend less

than 2 hours studying per lecture hour. I am done with the problem

Mr. Green. I have been following your videos throughout my stats class. I am so happy I found your videos. They are extremely useful and extremely helpful. Thank you for your help. You really made things quite easy to understand.

Mr. Green, I am very grateful for your video lessons. Everything about them has made the subject more understandable, from their length to the graphic details matching your narration. You give a straightforward subject a straightforward treatment, and skip no steps in your explanations. I especially appreciate this last aspect, as well as the fact that you avoid extraneous details and stick to the exercise at hand.