4There are good reasons for thinking that the time required to recover a normal

Question

4There are good reasons for thinking that the time required to recover a normal orning pulse rate after physical Ten people of similar age, sex and size were arbitrarily selected, asked to run at a moderat rate was measured on both morning and evening. The results (in mins) were as follows: activity maybe longer in the evening t han in the m e pace for 30mins and then the time each took to recover a normal pulse Person no. 23 5 678 9 10 Evening 5.3 7.1 6.4 6.6 4.7 3.6 6.5 4.9 3.4 4.0 Morning 4.5 6.9 65 4.73.2 4.0 5.0 5.4 2.0 4.1 The R output from two analyses of these data is presented below: Analysis 1 t. test (x-evening, y-morning, var. equal=T, paired-F) Two Sample t-test data: evening and morning t = 0 , 9899 , df 18, p-value 0 . 3353 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval -0.6958699 1.9358699 sample estimates mean of x mean of y 4.63 5.25 Analysis 2 t. test (x-evening, y-morning, var. equal=T, paired-T) Paired t-test data: evening and morning t= 2.1716 , df 9, p-value =0.05796 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval -0.02584928 1.26584928 sample estimates mean of the differences 0.62 (i) Which of these analyses is more appropriate? Give reasons for your answer (2 marks) ii What other checks would you need to carry out before deciding your pre- (3 marks) ferred analysis is applicable? (ii) Assuming these checks prove satisfactory, do the data provide evidence that time to recovery is larger in the evening that in the morning? (3 marks)

Explanation / Answer

i)
paired t-test is more appropriate
as the sample remains same in both case
morning and evening

iii)
p-value = 0.05796 for two-tailed test
p-value = 0.05796/2 = 0.02898 for right tailed-test
we reject the null hypothesis
the data provide evidence .

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