Question

You wish to test the following claim (HaHa) at a significance level of α=0.05α=0.05. For the context of this problem, one data set represents a pre-test and the other 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=137n=137 subjects. The average difference (post - pre) is ¯d=2.2d¯=2.2 with a standard deviation of the differences of sd=43.1sd=43.1.

1. What is the test statistic for this sample?
   
   test statistic =  Round to 4 decimal places.
   
2. What is the p-value for this sample? Round to 4 decimal places.
   
   p-value =  
   
3. The p-value is...
   • less than (or equal to) αα
   • greater than αα
   
   
4. This test statistic leads to a decision to...
   • reject the null
   • accept the null
   • fail to reject the null
   
   
5. 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

The hypotheses are

These are paired samples as the pre and post test results are obtained for the same subjects

From the sample we have

n=137 is the sample size

is the average difference (post - pre)

is the  standard deviation of the differences

We estimate the population standard deviation of the differences using the sample

The standard error of the mean difference is

The hypothesized value of mean difference is

The sample size n is greater than 30 and hence we can use normal distribution as the sampling distribution of mean difference. That means we will be doing a z test.

The test statistics is

ans: test statistic = 0.5975

This is a 2 tailed test (the alternative hypothesis has "not equal to")

The p-value is

ans: The p-value for this sample is 0.5485

ans: The p-value is...

• greater than α

We will reject the null hypothesis if the p-value is less than alpha. Here, the p-value is greater 0.05 and hence we fail to reject the null hypothesis.

ans: This test statistic leads to a decision to...

• fail to reject the null

As such, the final conclusion is that...

• 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.