A researcher randomly selects 6 fathers who have adult sons

A researcher randomly selects 6 fathers who have adult sons and records the fathers? and sons? heights to obtain the data below. Determine if sons are taller than their fathers at the a ?0.1 level of significance. The normal probability plot and boxplot indicate that the differences are approximately normally distributed with no outliers. Observation 1 2 3 4 5 6 height of father (in inches) 66.4 71.6 69.972.8 67.3 67.1 height of son (in inches) 67.5 69.3 74.873.5 71.0 71.2 Using the differences (father?s height) - (son?s height), what is your conclusion regarding Ib? Reject H0 because to is greater than - t alpha. Reject H0 because to is less than - t alpha. Do not reject H0 because to is greater than - t alpha. Do not reject H0 because to is less than - t alpha.

Solution

Reject Ho because To is less than -ta

The test statisitc is

t= mean difference/(s/vn)

=-1.839

Given a=0.1, the critical value is t(0.1, df=n-1=6-1=5)=-1.48 (from student t table)

69.1833	mean Father
71.2167	mean Son
-2.0333	mean difference (Father - Son)
2.7090	std. dev.
1.1059	std. error
6	n
5	df