Question

You wish to test the following claim (HaHa) at a significance level of α=0.001α=0.001. For the context of this problem, μd=μ2−μ1μd=μ2-μ1 where the first data set represents a pre-test and the second data set represents a post-test.

      Ho:μd=0Ho:μd=0
      Ha:μd>0Ha:μd>0

You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain pre-test and post-test samples for n=12n=12 subjects. The average difference (post - pre) is ¯d=13.9d¯=13.9 with a standard deviation of the differences of sd=48.2sd=48.2.

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

The p-value is...

• less than (or equal to) αα
• greater than αα

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is greater than 0.
• There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is greater than 0.
• The sample data support the claim that the mean difference of post-test from pre-test is greater than 0.
• There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is greater than 0.

Answer 1

The mean of the difference = 13.9, and the standard deviation of the difference S_d = 48.2

= 0.001 and the degrees of freedom = number of pairs - 1 = 12 - 1 = 11

The Hypothesis:

H0: = 0

Ha: > 0 (Claim)

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The Test Statistic: Since sample size is small, and population std. deviation is unknown, we use the students t test.

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The p value: (Right tailed) at t = 0.999, degrees of freedom = 11. This value is found using online calculators.

The p value = 0.1696

Therefore p value (0.1696) is > (0.001),

This Lead to a decision of Fail to Reject The Null.

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The Conclusion:

Therefore Option 4: There is not sufficient sample evidence to support the claim that the mean difference of post test from

pre test is greater than 0.

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