Question

Anemia (low healthy blood cells or hemoglobin) has an important role in exercise performance. However, the direct link between rapid changes of hemoglobin and exercise performance is still unknown. A study investigated 18 patients with a blood disorder (beta-thalassemia). Participants in the study performed an exercise test before and the day after receiving a blood transfusion. Data are given in the table.

ID	Change in HB	Obese	RER > 1.1
1	-1.4	No	No
2	-1.5	No	No
3	-2	No	Yes
4	-2.1	No	No
5	-1.9	Yes	Yes
6	-1.6	Yes	No
7	-1.8	No	Yes
8	-0.8	No	Yes
9	-1	No	No
10	-1.2	No	Yes
11	-0.8	No	No
12	-1.5	Yes	No
13	-1.4	No	Yes
14	-2.6	No	Yes
15	-1.7	No	Yes
16	-2.6	No	Yes
17	-2.7	Yes	No
18	-1.5	Yes	No

2. Is obesity associated with a RER greater than 1.1?

a. State the Null Hypothesis

b. Which test statistic would you use and what is the observed value

c. What conclusion would you reach (justify)?

          

Answer 1

Is obesity associated with a RER greater than 1.1?

a.

Null Hypothesis: Obesity and RER > 1.1 are associated.

b. Which test statistic would you use and what is the observed value

Since we are dealing with the categorical variable, the chi-square statistic is used to test the hypothesis,

The Chi-square test of independence is performed to test the association between Obesity and RER > 1.1

Step 1: The observed values are,

	RER>1.1
Obesity	No	Yes	Total
No	5	8	13
Yes	4	1	5
Total	9	9	18

Step 2: The expected values are obtained using the formula,

	RER>1.1
Obesity	No	Yes	Total
No			13
Yes			5
Total	9	9	18

Step 3: The Chi-Square Value is obtained using the formula

Step 4: The critical value for the chi-square statistic is obtained from the chi-square distribution table for,

Where r is the number of rows and c is the number of columns in the table.

For significance level = 0.05 and degree of freedom = 1, the critical value is,

Step 5: Since the chi-square value is less than the critical value, It can be concluded that the null hypothesis is not rejected at a 5% significance level.

c)

Hence both the variables Obesity and RER > 1.1 are independent.