o 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. LOADING... Click the icon to view the table of data. Height of ​Father, Xi Height of​ Son, Yi   71.5 76.6 72.7 76.2 68.6 71.1 70.3 72.2 66.6 67.7 72.1 72.6 67.9 67.8 69.2 68.7 71.7 70.4 71.5 69.6 73.2 70.8 68.5 65.0 69.2 64.3

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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.
LOADING...
Click the icon to view the table of data.
Height of
​Father, Xi
Height of​ Son, Yi
 
71.5
76.6
72.7
76.2
68.6
71.1
70.3
72.2
66.6
67.7
72.1
72.6
67.9
67.8
69.2
68.7
71.7
70.4
71.5
69.6
73.2
70.8
68.5
65.0
69.2
64.3
PrintDone
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 sample size must be large.
 
C.
The sample size is no more than​ 5% of the population size.
 
D.
The differences are normally distributed or the sample size is large.
 
E.
The sampling method results in a dependent sample.
Let
di=Xi−Yi.
Write the hypotheses for the test.
 
H0​:
 
mu Subscript d Baseline not equals 0μd≠0
mu Subscript d Baseline equals 0μd=0
mu Subscript d Baseline greater than 0μd>0
mu Subscript d Baseline less than 0μd<0
H1​:
 
mu Subscript d Baseline equals 0μd=0
mu Subscript d Baseline less than 0μd<0
mu Subscript d Baseline not equals 0μd≠0
mu Subscript d Baseline greater than 0μd>0
Calculate the test statistic.
 
t0=nothing
​(Round to two decimal places as​ needed.)
Calculate the​ P-value.
 
​P-value=nothing
​(Round to three decimal places as​ needed.)
Should the null hypothesis be​ rejected?
 
 
Reject
Do not reject
H0
because the​ P-value is
 
greater than
less than
the level of significance. There
 
is
is not
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
0.01
level of significance.
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