Question

In Canada, do young males (Y) weigh more than older males (O) on average? To investigate this question, weights of fifteen 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) 85.40 78.60 6.80 Standard Deviation (kg) 15.70 19.50 17.70 12.87 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? cross out cross out Select one: O a. 28 and (0.10.0.50) b. 14 and (0.025, 0.05) c. 14 and (0.05, 0.10) d. 14 and (0.10.0.50) e. 28 and (0.20, 1.0) cross out ooo cross out cross out

Answer 1

df = n_1 + n_2 - 2 = 15 + 15 - 2 = 28

  Test Statistics

Since it is assumed that the population variances are equal, the t-statistic is computed as follows:

X1 - X2 (n-1)s +(12-1)=(1+ ) + - 2 T

$t = \frac{ 85.4 - 78.6}{\sqrt{ \frac{(15-1)15.7^2 + (15-1)19.5^2}{ 15+15-2}(\frac{1}{ 15}+\frac{1}{ 15}) } }$

t = 1.052

The p-value is p = 0.1509

a) is the correct answer