Question

You wish to test the following claim (H1) at a significance level of α=0.002. For the context of this problem, d=x2−x1 where the first data set represents a pre-test and the second data set represents a post-test.

      Ho:μd=0
      H1: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=178 subjects. The average difference (post - pre) is ¯d=3.1with a standard deviation of the differences of sd=20.7.

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

What is the P-value for this test? For this calculation, use the conservative under-estimate for the degrees of freedom as mentioned in the textbook. (Report answer accurate to four decimal places.)
P-value = ±±

The P-value is...

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

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

Answer 1

Sol:

Ho:μd=0
      H1:μd≠0

t=xd-0/sd/sqrt(n)

=(3.1-0)/(20.7/sqrt(178))

= 1.998027

test statistic = +1.998

df=n-1=178-1=177

=T.DIST.2T(1.998027,177)

=0.04724498

p value=0.0472

The P-value is...

greater than α

fail to reject the null

There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is not equal to 0.

test statistic = +1.998

p value=0.0472

The P-value is...

greater than α

fail to reject the null

There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is not equal to 0.