Question

To test the belief that sons are taller than their​ fathers, a student randomly selects 6 fathers who have adult male children. She records the height of both the father and son in inches and obtains the accompanying data. Are sons taller than their​ fathers? Use the a = 0.1 level of signifigance. Note that a normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.

Observation	1	2	3	4	5	6
Height of father​ (in inches), Xi	70.2	67.1	71.4	66.7	71.9	69.2
Height of son​ (in inches), Yi	73.5	69.3	67.3	67.0	67.6	75.0

(a) Choose the correct null and alternative hypotheses. Let d_i = Y_i -X_i

(b) What is the p-value?

p-value = (Round to three decimal places as needed)

(c) What is the correct conclusion?

Answer 1

The statistical software output for this problem is:

Paired T hypothesis test:
μ_D = μ₁ - μ₂ : Mean of the difference between Yi and Xi
H₀ : μ_D = 0
H_A : μ_D > 0
Hypothesis test results:

Difference	Mean	Std. Err.	DF	T-Stat	P-value
Yi - Xi	0.53333333	1.6638643	5	0.32053896	0.3808

Hence,

a) Hypotheses:

H₀ : μ_D = 0
H_A : μ_D > 0

b) p - Value = 0.381

c) Do not reject Ho. There is not sufficient evidence to conclude that sons are taller than their fathers.