Question

A researcher randomly selects 6 fathers who have adult sons and records the​ fathers' and​ sons' heights to obtain the data shown in the table below. Test the claim that sons are taller than their fathers at the alpha equals α=0.10 level of significance. The normal probability plot and boxplot indicate that the differences are approximately normally distributed with no outliers so the use of a paired​ t-test is reasonable.

Observation	1	2	3	4	5	6
Height of father​ (in inches)	71.5	68.2	74.3	67.6	66.7	74.4
Height of son​ (in inches)	73.1	66.3	74.8	69.2	64.4	73.1

Part 1) What are the hypotheses for the​ t-test? Note that population 1 is fathers and population 2 is sons.

Part 2) Find the test statistic.

Part 3) Find the​ P-value.

Answer 1

(1)

(2)

(3)