00:01
All right.
00:01
So for this question, we are given a case study, and it references this paper.
00:09
It's scholl at all.
00:11
I'm not sure of the year.
00:13
But basically, this group of researchers wanted to look at the relationship of gender and sense of direction to spatial orientation in an unfamiliar environment.
00:27
And so this is from a actual.
00:30
Published study.
00:33
And basically they wanted to look at the spatial orientation skills of 30 male students and 30 female students.
00:41
And they did this experiment where they took them to a park and had them point to the direction of south.
00:51
And so basically they pointed to the direction of south and then they took a protractor and measured the angle to the nearest degree.
01:00
And basically, we have a data set that shows the pointing error in degrees when these 15 female participants attempted to point south.
01:17
And so based on these data that we have of these 15 points right here, we want to, we need to answer a few questions.
01:26
And so basically, the women who, so this group of 15 women consider themselves to have a good sense of direction.
01:38
And so we want to see if they really do have a good sense of direction than they would by randomly guessing at the direction of cell.
01:48
And so first, we are asked to conduct a hypothesis test.
01:57
And answer the following question.
01:59
So our first question that we want to answer is if on average women who consider themselves to have a good sense of direction do not better than they would by just randomly guessing at the direction of south and what would their mean pointing error be.
02:15
All right.
02:16
So to answer this first question, let's think about, you know, out of 360.
02:27
Degrees, basically half of that is south, right? so from zero to 180, that would be north, and then negative, you know, 180 all the way, or 180 to 360 would be south.
02:44
So essentially, we have 180 degrees.
02:47
And if you point anywhere and there's 180 degrees out of that total 360, you would be correct in pointing to the south.
02:56
And so, so our mean there would be 180 divided by two.
03:02
And we would get 90 as our mean pointing error.
03:09
And so 90 degrees would be, we'll just write this down here, pointing error if we were just write this down here, pointing error 90 degrees if we were just randomly pointing towards the south.
03:30
And so we can see here in our actual data set.
03:34
These are the error degrees.
03:36
And i've just gone and calculated the mean and the standard deviation because we are going to need those later.
03:42
But basically, we're just going to use handy -dandy excel formulas to calculate those for us.
03:48
So we have our population mean right here.
03:51
And then we have our standard deviation of that population.
03:56
And so we can already see that the mean error of pointing degrees is less than our, you know, our pointing error if you were to just randomly point.
04:07
So we want to see if this is significant or not.
04:11
So basically our null hypothesis would state that there is no difference in these two, you know, population means.
04:21
And our alternate hypothesis is, yes, there is a difference in these two means and that these women actually do consider, well, they consider themselves fairly decent at, you know, spatial directions.
04:40
And we want to see if it is significantly greater than just randomly pointing.
04:47
So our next question, we are at.
04:51
To consider, let's see, we want to use a one mean t test to look at, you know, to see actually if there is a significant difference here.
05:08
And so it says we are looking at the 5 %.
05:15
Is that 5? yeah, okay.
05:16
So 5 % significant level.
05:18
So that means an alpha value of 0 .05.
05:22
And we're going to use that alpha value when we look up our critical value in our charts.
05:32
And so right here, this is just the formula that we're going to be using for our one sample t test and to calculate our critical z value.
05:44
And so we have all of the information that we need to plug in.
05:48
And i've just gone ahead and done this in the formula.
05:52
But just, you know, to go over this, basically we want to take the sample mean and subtract it by the population means.
05:59
So our sample mean, in this case, is this 90 degrees, which was our random pointing error.
06:05
And we're going to subtract our population mean, which was over here, the 55 .4, which we got from taking the average of this column right here.
06:16
And so we're going to do 90 minus, 55 .4, put parentheses around it.
06:22
And then we're going to divide that by the population standard deviation, which we calculated down here.
06:30
And then that is divided by the square root of our sample size, which is just the number of subjects, and we have 15 subjects here.
06:40
So the square root of 15 and then put parentheses around that whole denominator...