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.**

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