Assume that the paired data came from a population that is normally distributed.
ID: 3133002 • Letter: A
Question
Assume that the paired data came from a population that is normally distributed. Using a 0.05 significance level find d sd the t test statistic and the critical values to test the claim that ,-0 17 13 10 15 12 4 12 --15 (Round to three decimal plac d=|-1.5 (Round to three decimal places as needed.) d 3.505 (Round to three decimal places as needed.) s = 3.505 (Round to three decimal places as needed t = -1.210| (Round to three decimal places as needed.) 1210 (Round to three decimal places as needed) 4,2 = ± (Round to three decimal places as needed.)Explanation / Answer
a)
Let ud = u2 - u1.
Formulating the null and alternative hypotheses,
Ho: ud = 0
Ha: ud =/ 0
At level of significance = 0.05
As we can see, this is a two tailed test.
Calculating the mean of the differences (third column):
dbar = 1.5 [ANSWER]
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Calculating the standard deviation of the differences (third column):
s = 2.891995222
Thus, the standard error of the difference is sD = s/sqrt(n):
sD = 1.022474716 [ANSWER, STANDARD ERROR OF THE DIFFERENCE]
Do you mean sd as the standard error or the standard deviation of the differences? If it is the standard deviation, please use the previous value, 2.891995222.
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As t = [dbar - uD]/sD, where uD = the hypothesized difference = 0 , then
t = 1.467028941 [ANSWER, T VALUE]
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As df = n - 1 = 7
Then the critical value of t is, by using table or technology, [as this is a two tailed 0.05 level test at df = 7]
tcrit = +/- 2.364624252 [ANSWER]
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