Question

Given the following dataset

x	1	1	2	3	4	5
y	0	2	4	5	5	3

We want to test the claim that there is a correlation between xand y.

(a) What is the null hypothesis Ho and the alternative hypothesis H1?

(b) Using α= 0.05, will you reject Ho? Justify your answer by using a p-value.

(c) Base on your answer in part (b), is there evidence to support the claim?

(d) Find r, the linear correlation coefficient.

The level of cretaine phosphokinase (CPK) in blood samples measures the amount of muscle damage for athletes. At Jock State University, the level of CPK was determined for each of 25 football players and 15 soccer players before and after practice. The two groups of athletes are trained independently. The data summary is as follows :For football players :

n=25	before practice	after practice	difference(before-after)
mean	254.73	225.6	29.13
St.deviation	115.5	132.6	21.00

For soccer players :

n=15	before practice	after practice	difference(before-after)
mean	177.1	173.8	3.3
st.deviation	60.7	64.4	6.88

Assume that all the data above are normal, use the information above to answer problems 7 to 10.

7. Construct a 95% Confidence Interval for the difference in mean CPK values for foot-ball players and soccer players BEFORE exercises.

8. Construct a 95% Confidence Interval for the difference in mean CPK values for foot-ball players BEFORE and AFTER exercises.

9. Test the claim that the mean CPK level has DECREASED for soccer players AFTERexercise (compared to the mean BEFORE exercise), using α= 0.10.

10. AFTER practice, do football players have a DIFFERENT mean CPK values com-pared to soccer players? Test this claim by performing a hypothesis test, usingα= 0.10.

Answer 1

a)

Here we have to test that

Null hypothesis :

Alternative hypothesis :

where is population correlation coefficient.

	x	y	x*y	x^2	y^2
	1	0	0	1	0
	1	2	2	1	4
	2	4	8	4	16
	3	5	15	9	25
	4	5	20	16	25
	5	3	15	25	9
Total	16	19	60	56	79

n = 6

b)

Test statistic :

where

r = 0.5890 (Round to 4 decimal)

t = 1.458 (Round to 3 decimal)

Test statistic = 1.458

b)Level of significance = = 0.05

Degrees of freedom = n - 2 = 6 - 2 = 4

P value for = 0.05 and df = 4 from excel using function:

=T.DIST.2T(0.05,4)

= 0.2186 (Round to 4 decimal)

P value = 0.2186

Here p value >

So we do not reject H0.

c)

Conclusion : There is no sufficient evidence to claim that there is correlation between x and y

d)

From part (b) ,

Correlation coefficient = r = 0.5890