Question

You wish to test the following claim (HaHa) at a significance level of α=0.01α=0.01. 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=50n=50 subjects. The average difference (post - pre) is ¯d=−18.8d¯=-18.8 with a standard deviation of the differences of sd=39.2sd=39.2.

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

Answer 1

α=0.01, μd=μ2-μ1

      Ho:μd=0
      Ha:μd<0

n=50, d¯=-18.8 , sd=39.2

What is the test statistic for this sample?
test statistic =(d¯ - μd)/(s/√n)

= (-18.8 - 0)/(39.2/√50)

= -3.391

What is the p-value for this sample?
p-value = 0.0007

The p-value is...

• less than (or equal to) α

This test statistic leads to a decision to...

• reject the null

As such, the final conclusion is that...

• The sample data support the claim that the mean difference of post-test from pre-test is less than 0.