Question

One part of this question I am getting wrong. I'm assuming it's the test statistic? I got 1 for Question C, and I got 5.432 for question b, and I got B for question C.

An undergraduate student performed a survey on the perceived physical and mental health of UBC students for her term project. She collected information by asking students whether they are satisfied with their physical and mental health status. 129 male and 157 female UBC students were randomly chosen to participate in the survey. After finishing the survey, she presented the following tables in her term project paper.

For both sexes:

	Number of students
Perceived physical health, satisfied	229
Perceived physical health, not satisfied	57
Perceived mental health, satisfied	257
Perceived mental health, not satisfied	29

For male students:

	Number of students
Perceived physical health, satisfied	108
Perceived physical health, not satisfied	21
Perceived mental health, satisfied	110
Perceived mental health, not satisfied	19

For female students:

	Number of students
Perceived physical health, satisfied	121
Perceived physical health, not satisfied	36
Perceived mental health, satisfied	147
Perceived mental health, not satisfied	10

(a) To test independence of perceived physical health and sex, we want to use a chi-square model with  degree(s) of freedom.

(b) Compute the chi-square statistic used to test independence of perceived physical health and sex. Round your answer to 3 decimal places. For all intermediate steps, keep at least 6 decimal places.
Answer:

(c) Which of the following statements is correct based on the result of the Chi-square test?

A. At a 5% significance level, we reject the null hypothesis. There is strong evidence that perceived physical health and sex are associated.
B. At a 5% significance level, we do not reject the null hypothesis. There is little evidence that perceived physical health and sex are associated.
C. At a 5% significance level, we reject the null hypothesis. There is strong evidence that perceived physical health and sex are independent.
D. At a 5% significance level, we do not reject the null hypothesis. There is little evidence that perceived physical health and sex are independent.

Answer 1

Null hypothesis : H_o : perceived physical health and sex are independent

Alternative Hypothesis : H_a: perceived physical health and sex are not independent.

The data that corresponds to sex and perceived physical health are :

for male students

Perceived physical health, satisfied	108
Perceived physical health, not satisfied	21

For female students:

	Number of students
Perceived physical health, satisfied	121
Perceived physical health, not satisfied	36

Consolidating the above tables into a 2x2 table

Observed Counts/Frequency	Male	Female	Total
Perceived physical health, satisfied	108	121	229
Perceived physical health, not satisfied	21	36	57
Total	129	157	286

(a) Degrees of freedom = (Number of rows-1)x(Number of columns - 1)=(2-1)x(2-1)

(b)

Test Statistic

O : Observed Frequency

E: Expected Frequency

Expected frequency

E: Expected Count/Frequency	Male	Female
Perceived physical health, satisfied	(229*129) / 286=103.290210	(229*157) / 286=125.709790
Perceived physical health, not satisfied	(57*129) / 286=25.709790	(57*157) / 286 =31.290210

O	E	O-E	(O-E)2	(O-E)2/E
108.000000	103.290210	4.709790	22.182124	0.214755
121.000000	125.709790	-4.709790	22.182124	0.176455
21.000000	25.709790	-4.709790	22.182124	0.862789
36.000000	31.290210	4.709790	22.182124	0.708916
			Total	1.962915

chi-square statistic used to test independence of perceived physical health and sex = 1.962915

For 1 degree of freedom,

p-value =0.161202

Level of significance =5% ie. =0.05

As p-value : 0.1612 > :0.05, Fail to reject the null hypothesis.

(c) Which of the following statements is correct based on the result of the Chi-square test?

B. At a 5% significance level, we do not reject the null hypothesis. There is little evidence that perceived physical health and sex are associated.