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You wish to test the following claim (Ha) at a significance level of a = 0.001....

Question

You wish to test the following claim (Ha) at a significance level of a = 0.001....

You wish to test the following claim (Ha) at a significance level of a = 0.001. For the context of this problem, Md = PostTes

You wish to test the following claim (Ha) at a significance level of a = 0.001. For the context of this problem, Md = PostTest - PreTest where the first data set represents a pre-test and the second data set represents a post-test. (Each row represents the pre and post test scores for an individual. Be careful when you enter your data and specify what your pi and M2 are so that the differences are computed correctly.) Hoid = 0 H: .:Hd 70 You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: pre-test post-test 34.2 32.1 54.3 55.4 32.5 81.4 52.4 35.4 54.7 116.9 66.7 80.8 38.4 82.4 47.4 50.1 41.6 152.4 42.7 90.4 35.2 73 51.6 60.2 34.2 35.3 43.5 147 41.2 189.4 33.6 86.4 53.9 109.3 66.7 164.3 What is the test statistic for this sample? test statistic = 3.9165 x (Report answer accurate to 4 decimal places.) What is the p-value for this sample? p-value = .0011 0(Report answer accurate to 4 decimal places.)
Math Statistics And Probability
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Answers

As per Question ,

\ H_0 :\mu _d =0  

\ H_1 :\mu _d \neq 0

To find : test stastistics ?

Under \ H_0, n = 18

\frac{\overline{d}}{S_d/\ \sqrt{n}} \sim t_{n-1}

pre post (post-pre) =d d-dbar (d-dbar)^2
34.2 32.1 -2.1 -47.5 2257.3
54.3 55.4 1.1 -44.3 1963.5
32.5 81.4 48.9 3.5 12.2
52.4 35.4 -17.0 -62.4 3895.1
54.7 116.9 62.2 16.8 281.9
66.7 80.8 14.1 -31.3 980.4
38.4 82.4 44.0 -1.4 2.0
47.4 50.1 2.7 -42.7 1824.2
41.6 152.4 110.8 65.4 4275.7
42.7 90.4 47.7 2.3 5.2
35.2 73.0 37.8 -7.6 57.9
51.6 60.2 8.6 -36.8 1355.1
34.2 35.3 1.1 -44.3 1963.5
43.5 147.0 103.5 58.1 3374.3
41.2 189.4 148.2 102.8 10565.6
33.6 86.4 52.8 7.4 54.6
53.9 109.3 55.4 10.0 99.8
66.7 164.3 97.6 52.2 2723.7
dbar 45.4 Total 35691.9

\ S_d =  \sqrt\frac{\sum (d-\overline{d})^2}{n-1} == 45.82

`Test statistics becomes , by putting the values

\ t_{cal} = 4.2047

Now , for n-1 = 18-1 = 17 and we have two side test , hence \frac{\alpha}{2} = 0.0005 = 0.5% level

\ t_{tabulated} = 2.898

Hence , test statistics is greater than t- tabulated value ,So we have sufficient evidance to reject Ho.\

To find = P- value ?

p(\ t_{17} > 4.2047}) =  

From the table ,

p(\ t_{17} > 3.965}) = 0.0005

So, that the probability value of

p(\ t_{17} > 4.2047}) = 0.00059555

round to 4 decimal place , we get

p(\ t_{17} > 4.2047}) = 0.0006

Which is less than 0.001 , hance we have sufficient evidance to reject Ho.

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