Question

Children's Weight

Research suggest that the American children are heavier than the Australian children. To investigate this, a researcher collected two simple random samples of 300 six-year-old American boys and (denote this sample 1) 325 six-year-old Australian boys (denote this sample 2) and measures their weight in Kilograms.

Children's Weight THE UNIVERSITY OF MELBOURNE We are interested to test if the average weight is higher for American boys compared to the average weight of the Australian boys. Research suggest that the American children are heavier than the Australian children. To investigate this, a researcher collected two simple random samples of 300 six-year-old American boys and (denote this sample 1) 325 six-year-old Australian boys (denote this sample 2) and measures their weight in Kilograms. What is the p-value of the test? Hint: use Excel to find the p-value Summary Statistics: a. 0.9999 Samplel : Xi = 24.1 81 = 4.9 Sample2 : X2 = 22.5 s2 = 4.0 b. 0.000005 OC. 0.05 d. 0.025

Answer 1

Correct option:

b.    0.0000005

Explanation:

Pooled Standard Deviation (s_P) is given by:

(n1 1)s12(n2 1)s22 sP= n1n2 2

(300 1) x 4.92 + (325 1) x 4.02 4.4547 300 325 2

SE spV1/n1 1/n2)

4.4547 1/300 1/325 0.3567

Test Statistic is given by:

t = (24.1 - 22.5)/0.3567

= 4.4860

ndf = n1 + n2 - 2 = 300 + 325 - 2 = 623

One Tail - Right Side Test

By Technology, p value = 0.0000005

So,

Correct option:

b.    0.0000005