Question

1. Using the data given below, calculate the linear correlation between the two variables x and y.

X	0	3	3	1	4
y	1	7	2	5	5

(a)        .794                 (b) .878            (c) .497            (d) .543

2. Refer to question 4. Assume you are using a 0.05 level of significance; is there a

significant relationship between the two variables x and y?

1. Yes                        (b) no

3. The heights (in inches) and pulse rates (in beats per minutes) for a sample of 40 women were measured and the linear correlation coefficient was found to be -.458 (based on data from the National Health Examination Survey). Using a significance level of 0.05, can you conclude that there is a significant relationship between the heights and pulse rates of women?
   1. Yes                     (b) no

4. A scatterplot in which one variable decreases as another variable increases is an example of a:
   1. Positive correlation           (b) negative correlation

(c)   Curvilinear relationship       (d) No correlation

5. Refer to question 6. How would you describe the relationship between women’s’ heights and pulse rates?
   1. Women who are relatively taller tend to have higher pulse rates
   2. Women who are relatively shorter tend to have lower pulse rates
   3. Women with higher pulse rates are more likely to be taller than women with lower pulse rates.
   4. Women with lower pulse rates are more likely to be taller than women with higher pulse rates.

Answer 1

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	0	1	0	1	0
	3	7	9	49	21
	3	2	9	4	6
	1	5	1	25	5
	4	5	16	25	20
Total	11	20	35	104	52

Sample size: n = 5

Now,

The coefficient of correlation is :

Correct option is c.

Degree of freedom: df=n-2= 5-2 = 3

The critical value of r using critical value table is 0.878

Since r < 0.878 so there is no significant relationship between the variables.

Answer: no