In a study designed to test the \"truth\" to the theory that, on average, U.S. a
ID: 3380571 • Letter: I
Question
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:Explanation / Answer
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]