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 alphaequals0.05 level of significance.​ Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers. LOADING... Click the icon to view the table of data. Which conditions must be met by the sample for this​ test? Select all that apply. A. The sampling method results in an independent sample. B. The sampling method results in a dependent sample. C. The sample size must be large. D. The sample size is no more than​ 5% of the population size. E. The differences are normally distributed or the sample size is large. Let d Subscript iequalsUpper X Subscript iminusUpper Y Subscript i. Write the hypotheses for the test. Upper H 0​: ▼ mu Subscript d Baseline less than 0 mu Subscript d Baseline not equals 0 mu Subscript d Baseline equals 0 mu Subscript d Baseline greater than 0 Upper H 1​: ▼ mu Subscript d Baseline greater than 0 mu Subscript d Baseline equals 0 mu Subscript d Baseline less than 0 mu Subscript d Baseline not equals 0 Calculate the test statistic. t 0equals nothing ​(Round to two decimal places as​ needed.) Calculate the​ P-value. ​P-valueequals nothing ​(Round to three decimal places as​ needed.) Should the null hypothesis be​ rejected? ▼ Reject Do not reject Upper H 0 because the​ P-value is ▼ greater than less than the level of significance. There ▼ is not is sufficient evidence to conclude that sons ▼ are taller than are the same height as are shorter than are not the same height as their fathers at the 0.05 level of significance. Click to select your answer(s).

Height of ​Father, Upper X Subscript iXi	Height of​Son, Upper Y Subscript iYi
72.972.9	77.877.8
66.866.8	70.370.3
68.268.2	70.670.6
72.372.3	74.174.1
68.868.8	70.070.0
71.471.4	72.172.1
68.668.6	68.568.5
69.269.2	68.568.5
66.866.8	65.665.6
70.370.3	68.468.4
72.572.5	70.170.1
72.772.7	69.369.3
70.670.6	65.7

Answer 1

P value = 0.4959 at df = n-1 = 12

Since p value > 0.05 we fail to reject the null hypothesis.

There is no sufficient evidence to conclude that the heights of sons taller than the father.