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=12n=12 subjects. The average difference (post - pre) is ¯d=7.1d¯=7.1 with a standard deviation of the differences of sd=14.5sd=14.5.

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

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

The test statistic is...

• in the critical region
• not in the critical region

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

(a)

= 0.01

ndf = n - 1 = 12 - 1 = 11

One Tail - Right Side Test

So,From critical value of t = 2.718

So,

critical value = 2.718

(b)

SE = s_d/

= 14.5/ = 4.1858

Test statistic is:

t = /SE

= 7.1/4.1858 = 1.696

So,

Test statistic = 1.696

(c)

The test statistic is not in the critical region.

(d)

Correct option:

Fail to reject the null

(e)

Correct option:

There is not suffient sample evidence to support the claim that the mean difference of post - test from pre-test is greater than 0.