Question

A student counsellor is concerned about students’ stress levels. S/he wants to understand whether students in different courses have similar stress levels.

The following table shows a random sample of students in different courses and their stress levels (n= 208208). Use the table to answer the questions which follow.

	Stress Levels by Enrolment
Enrolment	Low	Normal	High
Law	24	48	49
Arts	25	34	28

1. (1 mark) What proportion of the students in the study have normal stress level? (3dp) Answer

2. (1 mark) What proportion of the Arts students have low stress level? (3dp) Answer

3. (1 mark) What proportion of the students have high stress levels were Law students? (3dp) Answer

The student counsellor would like to answer the following research question: Do students in different courses experience different stress levels? S/he sets up the following null and alternative hypotheses to answer the research question.

H0:H0: There is no association between enrolled course and level of stress. H1:H1: There is an association between enrolled course and level of stress.

4. (1 mark) What is the expected value for Law students who have low stress levels? (3dp) Answer

5. The absolute value of the test statistic is equal to (type your answer with 3 dp) Answer

6. (1 mark) The degrees of freedom is equal to (type your answer as an integer) Answer

7. (1 mark) The p-value is smaller than 0.05 Answertruefalse

8. (1 mark) We decide that Answerp value is greater than 0.05, therefore we do not reject the null hypotesisp value is less than 0.05, therefore we reject the null hypotesis

9. (2 mark) Our conclusion is that AnswerThere is no association between enrolled course and level of stress.There is an association between enrolled course and level of stress.

10. We are 95% confident that proportion of students with normal stress level for Arts is between Answer (lower limit) and Answer (upper limit). Type your answers with 3dp.

Answer 1

(1) proportion of the students in the study have normal stress level = (48+34)/208 = 0.394.
(2) proportion of the Arts students have low stress level = 25/(25+34+28) = 0.287.
(3) proportion of the students have high stress levels were Law students = 49/(49+28) = 0.636.

(4) Expected values are calculated using the formula: (row total * column total)/grand total. Here, expected value for Law students who have low stress levels = (49 * 121)/208 = 28.505.
(5) Observed values = O = (24,25,48,34,49,28). Expected values = E = (28.505,20.495,47.702,34.298,44.793,32.207).
Now, test statistic = = 2.651.
(6) Degrees of freedom = (no. of rows - 1)*(no. of columns - 1) = 1 * 2 = 2.
(7) p-value = 0.266 -> FALSE.
(8) We decide that p value is greater than 0.05, therefore we do not reject the null hypothesis.
(9) Our conclusion is that -> There is no association between enrolled course and level of stress.