Question

To test the belief that sons are taller than their​ fathers, a student randomly selects 13 fathers who have adult male children. She records the height of both the father and son in inches and obtains the following data. Are sons taller than their​ fathers? Use the α=0.01 level of significance.​ Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.

Height of Father(Xi) Height of Son(Yi)
70.5 75.6
67.8 71.4
71.4 73.9
69.9 71.6
67.7 68.9
68.3 68.9
69.4 69.5
71.8 71.2
66.8 65.5
69.3 67.5
72.7 70.3
72.5 69.0
71.8 66.7

Which conditions must be met by the sample for this​ test? Select all that apply.

A. The sample size is no more than​ 5% of the population size.

B. The sample size must be large.

C. The sampling method results in an independent sample.

D. The sampling method results in a dependent sample.

E. The differences are normally distributed or the sample size is large.

Let di=Xi−Yi. Write the hypotheses for the test.

H0​: (μd≠0, μd<0, μd>0, μd=0)

H1​: (μd=0, μd≠0, μd>0, μd<0)

Calculate the test statistic.

t0=____ ​(Round to two decimal places as​ needed.)

Calculate the​ P-value.

​P-value=____ ​(Round to three decimal places as​ needed.)

Should the null hypothesis be​ rejected?

(Reject, Do not reject) H0 because the​ P-value is (less than, greater than) the level of significance. There (is, is not) sufficient evidence to conclude that sons (are the same height as, are taller than, are not the same height as, are shorter than) their fathers at the 0.01 level of significance.

Answer 1

The statistical software output for this problem is:

Hence,

Conditions:

D. The sampling method results in a dependent sample.

E. The differences are normally distributed or the sample size is large.

H₀ : μ_D = 0
H_A : μ_D < 0

Test statistic = -0.01

P-value = 0.496

Do not reject; Greater than; is not; are taller than