Question

4. The effect of exercise on the amount of lactic acid in the blood was examined. Blood lactate levels were measured in eight males before and after playing three games of soccer. The data below was measured Player Before After Difference 1 13 18 -5 2 20 37 -17 3 17 40 -23 4 13 35 -22 5 13 30 -17 6 16 20 -4 7 un 33 18 00 16 19 -3 Table 2 where the mean difference is -13.63 with standard deviation of 8.28. We wish to test if there is an increase in lactate levels at significance level of 0.05. Answer the question below (a) Is this a paired data? Briefly explain your answer. (b) Suppose we tag the sample before playing the three games as "sample 1" so "sample 2" is after the three games, and we define Hdif = 12 - M1. State the null and alternative hypothesis. (c) Assuming all assumptions are met, perform the hypothesis test using a test statistic ap- proach

Answer 1

part a)

yes it is paired data because it is before and after observations on same sample.

part b)

here we have before and after mean difference

0 !!! : ("Himu

$alternative (H_1): \mu _{diff}> 0$

part c)

Here we already have mean of difference column is

So t = (sample mean -0)/ (sample standard deviation/sqrt(n))

where sample mean = 13.63 as we are taking mean diff = mu2 - mu1 , n=8,sample std.dev = 8.28

so t = 13.63/(8.28/sqrt(8))

t = 13.63/2.9274

t= 4.66

as this is right tailed test from p-value is right taile area from 4.66 and above

to calculate p-value we will use excel coomand as follows and press enter

=T.DIST.RT(4.66,7)

this will gives us right tailed p-value using t-statistics(x) 4.66 and degrees of freedom = n-1 = 8-1 =7

it will gives us 0.001157

The given significance level is 0.05

and p-value is 0.001157

as p-value is less than 0.05

we have to reject null(H0)

And suport H1 so we can conclude that there is an increase in a lactic level