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 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) 65.2 69.1 68.2 68.6 67.9 68.6
Height of son (in inches) 65.1 68.9 66.1 67.3 69.2 70.2
a. What are the hypotheses for the t-test? Note that population 1 is fathers and population 2 is sons.
b. Find the test statistic. (Round to three decimal places as needed.)
c. Find the P-value. (Round to four decimal places as needed.)
d. What is the correct conclusion for the hypothesis test?
