00:01
This question looks at the results of a survey.
00:03
Who is the best james bond? so you can see that we have a list of six actors.
00:09
I abbreviated their names here.
00:12
We have six actors and the frequency with which each was selected looks like a total of 211 respondents.
00:20
So our question is, at a 5 % level of significance, is there evidence of a difference in popularity? so let's think about what the hypotheses would be.
00:30
The null hypothesis would state that there's no difference in popularity among the six actors.
00:36
Or in other words, all six proportions are equal and they're all equal to one over six.
00:43
The alternative hypothesis would state that there is a difference in popularity, that is that some pi is not equal to pj.
00:53
The expected counts then would simply be one over six times the total number of respondents it's 211, and that gives us 35 .17.
01:06
And you can see that i just wrote that then up in parentheses here on the table just next to the observed counts.
01:15
So let's take a look at how we would answer this question.
01:18
Is there evidence of a difference in popularity? well, we need to calculate the kai square statistic.
01:25
And to calculate the kai square statistic, we will take four.
01:30
Each one of these actors, the observed minus the expected value will square the difference and divide by the expected value.
01:38
So you can see that i wrote that out here.
01:41
We have six different terms.
01:43
They work out to be 112 .2 and so on for a total of 171 .9.
01:53
That is quite a large kai square statistic.
01:56
Before we proceed, we should do a quick check on the values here, notice that all of the values in the table, the observed counts, are at least five.
02:08
So we are okay to proceed with this test.
02:11
The degrees of freedom is simply the number of cells minus one, so that's six minus one or five degrees of freedom.
02:19
So once we have our kai square statistic and the degrees of freedom, now we'll use technology, either stat key or a graphing calculator, and we'll find the piece.
02:30
Value.
02:31
So on stat key, you'd go to theoretical distribution and choose kai square.
02:37
And when you choose kai square, you'll then get to a screen that asks you to edit the parameters.
02:43
That's where you'll first enter your degrees of freedom five.
02:47
You'll select a right -tailed test.
02:51
And then at the horizontal axis, you'll enter your kai square statistic of 171 .9.
02:59
And then the result, you'll enter the the result will show right here in the middle portion of the graph.
03:03
That's our p value, which rounds to 0 .000.
03:07
Graph and calculator will give you the same results.
03:11
You'll just go into the distribution command.
03:14
So second distribution, you'll choose kai square cdf.
03:19
The lower limit will be the kai square statistic.
03:22
The upper limit would be a much larger number.
03:25
I picked 99.
03:27
There's our five degrees of freedom.
03:29
And when you press, enter and paste and then enter, excuse me, you'll end up with a result that also, that looks like it got cut off just a little bit...