In a study designed to test the truth to the theory that on

In a study designed to test the \"truth\" to the theory that, on average, U.S. adults gain weight between Thanksgiving and January a research team looked at responses from 8 randomly selected U.S. adults. The subjects were weighed (lb) on the day before Thanksgiving and again on January 3^rd The raw data are found in Table Let alpha = 0.05 Fill in the missing table cells for the weight differences per the directions outlined in the bottom caption. The appropriate null/alternative hypothesis pair for this study is:

Solution

A)

The numbers on the last row, subtracting the first row from the second row are

3.8
4.2
2.7
4.7
3.9
3.1
7.3
-0.7 [ANSWER]

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b)

Let ud = u2 - u1.              
Formulating the null and alternative hypotheses,              
              
Ho:   ud   <=   0  
Ha:   ud   >   0   [OPTION A]

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c)

At level of significance =    0.05          
As we can see, this is a    right   tailed test.      
              
Calculating the standard deviation of the differences (third column):              
              
s =    2.522204423          
              
Thus, the standard error of the difference is sD = s/sqrt(n):              
              
sD =    0.891733926          
              
Calculating the mean of the differences (third column):              
              
XD =    3.625          
              
As t = [XD - uD]/sD, where uD = the hypothesized difference =    0   , then      
              
t =    4.065113927 = 4.07   [ANSWER, TEST STATISTIC]

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d)

As df = n - 1 =    7          
              
              
Also, using p values, using technology,              
              
p =        0.002389309 = 0.0024 [ANSWER]

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e)      
              
As P < 0.05, WE REJECT THE NULL HYPOTHESIS.   [ANSWER, OPTION D]