Question

You wish to test the following claim ( H 1 ) at a significance level of α = 0.01 . For the context of this problem, μ d = μ 2 − μ 1 where the first data set represents a pre-test and the second data set represents a post-test. H o : μ d = 0 H 1 : μ d ≠ 0 You believe the population of difference in scores is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: pre-test post-test 47.7 -6.1 33.1 -10.7 57.2 65.3 51.3 63 38.2 23.4 68.8 31.6 27.7 22.3 37.2 50.3 34.2 3.3 72.6 45.4 What is the test statistic for this sample? (Report answer accurate to 2 decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to 4 decimal places.) p-value = The p-value is... less than (or equal to) α greater than α 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 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

Answer 1

GIVEN:

The following sample of data on pre test and post test:

Pre test	Post test
47.7	6.1
33.1	10.7
57.2	65.3
51.3	63
38.2	23.4
68.8	31.6
27.7	22.3
37.2	50.3
34.2	3.3
72.6	45.4

HYPOTHESIS:

Let is the true difference in scores in population.

The hypothesis is given by,

(That is, there is no significant mean difference between pre test and post test)

(That is, there is significant mean difference between pre test and post test)

LEVEL OF SIGNIFICANCE:

TEST STATISTIC:

which follows t distribution with degrees of freedom

where is the mean of difference between pre test and post scores and

is the standard deviation of the difference between pre test and post scores.

CALCULATION:

Let us first calculate the difference between the two scores.

Pre test	Post test	Difference
47.7	6.1	-41.6
33.1	10.7	-22.4
57.2	65.3	8.1
51.3	63	11.7
38.2	23.4	-14.8
68.8	31.6	-37.2
27.7	22.3	-5.4
37.2	50.3	13.1
34.2	3.3	-30.9
72.6	45.4	-27.2

I have used excel function to calculate the mean and standard deviation of difference .

Mean: "=AVERAGE(select array of data values)"

Standard deviation: "=STDEV(select array of data values)"

The mean of difference between pre test and post scores

The standard deviation of the difference between pre test and post scores

Sample size

Now

P VALUE:

The two tailed p value for test statistic with degrees of freedom is,

  

  

  

  

The p value is .

DECISION RULE:

CONCLUSION:

Since the calculated p value (0.0502) is greater than the significance level , we fail to reject the null hypothesis and conclude that there is no significant mean difference between pre test and post test. That is, there is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is not equal.