Question

You wish to test the following claim (HaHa) at a significance level of α=0.001α=0.001. 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=50n=50 subjects. The average difference (post - pre) is ¯d=−6.7d¯=-6.7 with a standard deviation of the differences of sd=23.8sd=23.8.

1. What is the test statistic for this sample?
   
   test statistic =  Round to 3 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 less than 0.
   • There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is less than 0.
   • The sample data support the claim that the mean difference of post-test from pre-test is less than 0.
   • There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is less than 0.

Answer 1

Solution:

Test stat can be calculated as

Test Stat = (Dbar - muD)/SD/sqrt(n)

Here Dbar = -6.7

SD = 23.8

Test Stat = (-6.7-0)/23.8/sqrt(50)

Test Stat = -6.7/3.366 = -1.991

DF = 50-1 =49

p-value from t table is 0.0261

here alpha = 0.001

Here we can see that p-value is greater than alpha value(0.0260>0.001)(p-value>Alpha value)

In this test statistic we are failed to reject the null hypothesis as p-value is greater than alpha value.So its answer is C. i.e. fail to reject the null hypothesis.

As such the final conclusion is that the sample data support the claim that the mean difference of post from pre test is less than 0. So its answer is C.