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=0.025 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   Height of Son
67.9    73.0
70.7    74.2
71.8    74.3
71.6    73.5
69.4    70.6
67.7    68.2
70.6    70.5
70.2    69.6
68.5    67.3
70.8    69.1
68.1    65.7
69.3    65.8
69.6    64.5

Which conditions must be met by the sample for this​ test?

Select all that apply.

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

B. The sample size must be large.

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

D. The sampling method results in an independent sample.

E. The sampling method results in a dependent sample.

Answer 1

The test which can be used hereto test the hypothesis is the matched pair t-test.

A. This condition is required since the matched pair t-test either the differences should be normally distributed or the sample size should be large.

B. This condition is not required since the matched pair t-test works well with small samples too.

C. This condition is not required. The sampling population could be more than 5% of the population size.

D. This condition is not required since for the matched pair t-test we need a dependent sample rather than an independent sample.

E. This condition is required since for the matched pair t-test, we need a dependent sample.

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