Below is a random sample of shoe sizes for 12 mothers and th

Below is a random sample of shoe sizes for 12 mothers and their daughters.

Calculate the difference between the daughters\' and mothers\' shoe sizes given below. (Leave no cells blank - be certain to enter \"0\" wherever required. Round your answers to 1 decimal place.)

Calculate the mean and standard deviation for the difference. (Round your answers to 4 decimal places.)

Solution

A-1.

The diferrences are

1
1
0
0
0.5
0.5
1
1.5
3
0
0
1 [ANSWERS]

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a-2)

Formulating the null and alternative hypotheses,              
              
Ho:   ud   <=   0  
Ha:   ud   >   0  
At level of significance =    0.01          
As we can see, this is a    right   tailed test.  
Calculating the mean of the differences (third column):              
              
XD =    0.791666667   [ANSWER]      

  
              
Calculating the standard deviation of the differences (third column):              
              
s =    0.864931246   [ANSWER]      

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a-3.

As this is right tailed,

a. REJECT HO IF T > 2.718. [ANSWER]

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a-4.
              
Thus, the standard error of the difference is sD = s/sqrt(n):              
              
sD =    0.249684144          
              
              
As t = [XD - uD]/sD, where uD = the hypothesized difference =    0   , then      
              
t =    3.170672572   [ANSWER]

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b-1.      

It is not close. [ANSWER]

Also, using p values,              
              
p =        0.004453968   [ANSWER]  

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b-2.

As P < 0.01, TRUE. [ANSWER]

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b-3.

Still, by our results,TRUE. [ANSWER]