00:01
Hey there, welcome to numerate.
00:04
So we have a student academic group challenging the college campus, claiming their freshman students study at least 2 .5 hours per day.
00:13
And the stats class of the student academic group is skeptical, right? so actually, let me read this again.
00:21
So we have a stats class that is skeptical about the student academic group.
00:26
So we're trying to test the claim for a student academic group.
00:31
Which is basically the noaa hypothesis.
00:33
So we're given a sample size, sample mean, and sample standard deviation.
00:37
So therefore, that implies we will be using a t -statribution.
00:41
So our noaa hypothesis will be the student academic group, so where the mean, which denoted as mean, population mean, is at least, so greater than equal to 2 .5.
00:53
So since our data over here is given minutes, we have transformed the 2 .5 into, minutes.
01:02
So 2 .5 minutes will basically be 250 minutes because we have, let's see, so we have 60 minutes, 150.
01:13
60 minutes in an hour times 2, that would be 2 hours, so 120 minutes plus 30 because half an hour is 30 minutes.
01:22
So 220 plus 30 equals 150.
01:25
So perfect.
01:27
And then we have ha.
01:35
Ha will be the opposite where mu is less than 150.
01:40
Okay, usually the alternative is the opposite of our null, so it should be less than.
01:46
So looking at this, this will be a left -tail test, so let's put in our values here.
01:51
So we have a mean of 137.
01:53
We're looking at 150 minutes for the hypothetical mean, divided by our standard deviation here, standard deviation is 45 minutes, divided by the square root of n.
02:04
All right, so square root of n is our sample size of 30 students.
02:15
So let's calculate our t score here...