00:01
We're doing a hypothesis test to see if students are a good judge of how long a minute is.
00:05
And so we're going to assume that the mean of the students, when they guess the time is going to be 60 seconds, and alternately it's not 60 seconds.
00:14
So we're doing a two -sided test.
00:17
And i put my data into the calculator into my list, and i found that the mean of those 15 numbers was 62 .6 repeating, that the standard deviation of those numbers was 19 .481, and that that sample size was 15.
00:36
And so we're assuming that 60 is the main for those students.
00:46
Now, obviously, we're getting a number that's higher, 62 .6 repeating.
00:50
And we want to test and see if this is something that's unusual.
00:55
But since it's a two -tail test, our p value will not only be this end, but it will be this end that is symmetrically located on the opposite side.
01:05
So let's find the probability of if the mean is 60, having a sample of size 15, and getting a mean that is greater than or equal to 62 .6 repeating, and really, or less than are equal to, and this is 2 .2 and 2 thirds.
01:24
So if we subtract 2, that's 58 and subtract 2 thirds, that would be 57 and a third.
01:30
So that's where this other number is.
01:32
And so how likely is it to get either this or this happening if the mean is actually 60? so we're just going to find one tail and double that to find our p value.
01:43
So let's get our test statistic.
01:46
Our test statistic is a t value with 14 degrees of freedom.
01:49
And we know we take what we got, minus the mean.
01:55
Which is 60 divided by the standard deviation over the square root of n.
02:03
And i've already put that into my calculator to get that value...