Question

In Canada, do young males (Y) weigh more than older males (O) on average? To investigate this question, weights of twenty males randomly selected from each group were recorded. Summary statistics are given in the following table. Assume weight of each group follows a normal distribution. (If you think the samples are independent, then assume equal variances.)

Summary statistics	Young (Y)	Old (O)	Pooled	Difference
Average (kg)	87.32	78.60		8.72
Standard Deviation (kg)	14.80	18.40	16.70	5.28

What will be the respective degrees of freedom and the P-value range for testing if young Canadian males weigh more than older males on average?

Select one:

a. 38 and (0.05, 0.10)

b. 38 and (0.20, 1.0)

c. 19 and (0.10, 0.50)

d. 38 and (0.10, 0.50)

e. 19 and (0.05, 0.10)

Answer 1

let X, denotes the weight of and X₂ denotes the weight of we have. younger males alder males. X=87.32 S. a 14.80 no - 20 X2 = 78.60 S₂ = 18.40 1₂ = 20 of= n, +4₂-2 - 20+20-2 238. We have to test Ho: M. - Ma vs. H. Mi > M . which corresponds to a right-tailed t-test. Test statistic is X-X₂ (n-1) 52 + (021) 52 nith₂-2 87.32-78.60 = 1.651 19( 14.80² + 18.40²) L 3820) p-value = P(tze > 1.651) = 0.0534. So, option (a) is correct. 38