As part of a study into healthy lifestyles, Jing visited...

As part of a study into healthy lifestyles, Jing visited Surrey Hills University. Jing recorded a person's position in the university and how frequently they ate a salad. Results are shown in the table. egin{tabular}{|l|c|c|c|c|} cline { 2 - 5 } multicolumn{1}{c|}{} & multicolumn{4}{c|}{ Salad meals per week } \ cline { 2 - 5 } multicolumn{1}{c|}{} & ( mathbf{0} ) & ( mathbf{1 - 2} ) & ( mathbf{3 - 4} ) & ( mathbf{> 4} ) \ hline Students & 45 & 26 & 18 & 6 \ hline Professors & 15 & 8 & 5 & 12 \ hline Staff and Administration & 16 & 13 & 10 & 6 \ hline end{tabular} Jing conducted a ( chi^{2} ) test for independence at a ( 5 % ) level of significance. (a) State the null hypothesis. (b) Calculate the ( p )-value for this test. (c) State, giving a reason, whether the null hypothesis should be accepted.

Transcript

0:00 Hi there.

00:01 So for this problem, the first thing that we need to answer for this is the null hypothesis or h -0.

00:09 So the new hypothesis for this is that there is no association between a person's position in the university and the frequency of salad consumption.

00:48 Per week.

00:52 In other words, the two variables position in cellar consumption frequency are independent.

00:58 So that will be the null hypothesis for this.

01:02 Now, let's solve 4b of this problem.

01:04 Now, for par b, we will need the information that we were given in this table.

01:09 So then with the information that we are given, the first thing, to calculate the pali for this test, first of all, we need to obtain the expected frequencies.

01:20 The expectation frequencies is the row total times the column total and then this divided by the grand total.

01:35 So what do you need to do is for the student zero, you just need to add, for the students with a value of zero in the cell of meals, you just first you need to the row total will be the sum of the values that you are given in there so for that case that will be 45 plus 26 .18 hi there so for this problem so for example for zero will be 95 times 76 for the column and this divided by the grand total the grand total the grand total will be 187.

02:27 This is when we add all of the values in this table.

02:30 So this will give us a value of 38 .64.

02:35 Now you just need to do this for each row for this.

02:40 For example, when we are at the professor 1 -2, okay, so the professor 1 -2, if you add on the values in the columnar form, in a glute nor form, we will obtain 47.

02:56 And then this times 54 for the, oh, sorry, 47 for the row, 54 for the column.

03:03 And this divided by 187, so that will give us a value of 13 .57.

03:08 And then for the order, we will have 45 times 24 divided by 187.

03:14 So that will give us a value of 5 .78.

03:17 So once you calculate all of this, you just can fill up the table with the values.

03:25 For example, we have students, then we have zero, one to two, three, to four, or greater than four.

03:34 And then we will have our students.

03:36 For the first one is 38 .64...

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