Hypothesis testing with paired differences

Question

You wish to test the following claim (HaHa) at a significance level of α=0.1. 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=5 subjects. The average difference (post - pre) is d¯=-11.9 with a standard deviation of the differences of sd=11.925.

What is the critical value for this test? (Report answer accurate to three decimal places.) 

critical value = ±±

What is the test statistic for this sample? (Report answer accurate to three decimal places.) 

test statistic =

Answer 1

sd = 11.925

sample mean difference= 11.9

n=5

matched pair design

dependent t test statistic

assume Ho: population mean difference= 0

alternative Ha: difference does not =0,

2 tailed test

degrees of freedom = df =N-1 = 5-1=4

use alpha=.05, if not otherwise specified

but it is specified as .10

2 tailed, .10, df=4

use those 3 variables to find t critical value on t tables

t crtical = 2.132

t critical = 2.776 for alpha =.05

in either event, fail to reject Ho

then calculate t observed = t calculated

compare it to t critical value

if larger, reject Ho

t observed = 11.9/11.925/sqr(5-1) = 23.8/11.925 = about 1.9958

compare it to t critical

1.9958<2.132

t observed < t crticial

fail to reject Ho

Answer 2