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 0.10α=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)	73.5	69.9	65.9	70.8	67.4	68.1
Height of son​ (in inches)	71.4	71.7	70.6	75.0	71.7	69.4

Find the critical​ value(s).

Find the test statistic.

Answer 1

Given :-

Sample 1 = Height of son

Sample 2 = Height of father

The following table is obtained:

	Sample 1	Sample 2	Difference = Sample 1 - Sample 2
	71.4	73.5	-2.1
	71.7	69.9	1.8
	70.6	65.9	4.7
	75.0	70.8	4.2
	71.7	67.4	4.3
	69.4	68.1	1.3
Average	71.633	69.267	2.367
St. Dev.	1.868	2.715	2.606
n	6	6	6

From the sample data, it is found that the corresponding sample means are: