Question

ou wish to test the following claim hypotheses at a significance level of α=0.02

      H0:μd=0H0
      HA:μd<0HA

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.

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=42n=42 subjects. The average difference (post - pre) is ¯d=−1.2 with a standard deviation of the differences of sd=16.2

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

t=

What is the degree of freedom for this sample?

df=

The pp-value is...

• less than (or equal to) αα.
• greater than αα.

Answer 1

Solution:

Given in the question

Null hypothesis H0: D = 0

Alternate hypothesis Ha: D <0

This is left tailed test and one tailed test

Also Level of significance () = 0.02

Dbar = -1.2

SD = 16.2

Sample size n = 42

Here population is normally distributed so we will use paired t test

Test statistic can be calculated as

Test stat = (Dbar - d)/SD/sqrt(n) = (-1.2-0)/16.2/sqrt(42) = -1.2/2.5 =-0.48

From t table we found p-value as df = n-1 = 42-1 = 41, also this is one tailed and left tailed test so p-value from t table is 0.3169

Here we can see that p-value is greater than alpha value (0.3169>0.02) so we are failed to reject the null hypothesis.