Question

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

      Ho:μd=0
      Ha: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=16 subjects. The average difference (post - pre) is ¯d=19.3 with a standard deviation of the differences of sd=28.6

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

Claim: To check whether the population mean difference in the pre-test and post-test is greater then zero.

The Hypothesis is

v/s

Where,

=Population mean of Pre test data

=Population mean of post test data

This is right (one) tailed test as our interest is to see

Now,

n= Number of subjects =16
= sample mean of differences (post-pre)= 19.3

Sd= sample standard deviation of differences = 28.6

Now, we can find the test statistic

T-statistics=

=

= 2.699

Test statistics is 2.699

Now, we find the P-value

Degrees of freedom = n-1= 16-1=15

= level of significance=0.001

this is one tailed test

P-value =0.0082  ( using EXCEL =TDIST(|t-statistics=2.699,D.F=15,tail=1))

Decision:

P-value > 0.001 ()

Since, the P-value greater than the value of 0.001 ()

we fail to reject the Null hypothesis Ho.

Conclusion:

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