Question

You wish to test the following claim (Ha) at a significance level of α=0.001. d denotes the mean of the difference between pre-test and post-test scores.     

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=127 subjects. The average difference (post - pre) is ¯d=−6.8 with a standard deviation of the differences of sd=24.7

1. The test statistic's value is (-6.8-0)/(24.7/sqrt(127)) = -3.103.
   What is the test statistic for this sample?
   • t, df = 0
   • paired samples t-test, df = 126
   • t, df = 24.7
   • z
   • independent samples t-test, df = 126
   
   
2. What is the p-value for this sample? Round to 4 decimal places.
   p-value =
   
   
3. The p-value is...
   • greater than α
   • less than (or equal to) α
   
   
4. This test statistic leads to a decision to...
   • accept the null
   • fail to reject the null
   • reject the null
   
   
5. As such, the final conclusion is that...
   • The sample data support 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.
   • 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 sample evidence to support the claim that the mean difference of post-test from pre-test is less than 0.

Answer 1

Here given n = 127

mean difference () = -6.8

Standard deviation of sample difference (s_d ) =24.7

We need to use the Student's t- distribution