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
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