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=25n=25 subjects. The average difference (post - pre) is ¯d=−22.8d¯=-22.8 with a standard deviation of the differences of sd=27.8sd=27.8.

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 =

The test statistic is...

• in the critical region
• not in the critical region

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

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

answer)

Ho : ud = 0

Ha : ud < 0

Degrees of freedom is = n-1, 24

For df 24 and alpha 0.001 critical value from t table is = -3.467

Critical value is -3.467

Rejection region is if t < -3.467 reject the null hypothesis

Test statistics is = (d)/(Sd/√n)

D = -22.8

Sd = 27.8

N = 25

After substitution

Test statistics is = -4.101

As test statistics is less than -3.467

Test statistics is in the critical region

So, the test statistics leads to a decision to reject the null

There is sufficient evidence to support the claim that mean difference is less than 0