Question

1. You wish to test the following claim (Ha) at a significance level of α=0.005. For the context of this problem, μd=μ2−μ1where 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=49n=49 subjects. The average difference (post - pre) is ¯d=4.5 with a standard deviation of the differences of sd=14.2.

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

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

2. You wish to test the following claim (HaHa) at a significance level of α=0.002α=0.002. 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=124 subjects. The average difference (post - pre) is ¯d=1.5 with a standard deviation of the differences of sd=27.2.

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

1.

μ_d = μ₂−μ₁

(Two Tailed test)

Sample Mean of the differences :	4.5
Sample Standard Deviation of the differences : sd	14.2
Sample Size : n	49
Level of significance :	0.005
Degrees of Freedom : n-1	48

test statistic = 2.218

p-value for two tailed test

test statistic : = 2.218

P(t>2.2183)=T.DIST.RT(2.2183, 48)=0.0156 (Excel function T.DIST.RT)

p-value = 0.0312

T.DIST.RT function
Returns the right-tailed Student's t-distribution.
The t-distribution is used in the hypothesis testing of small sample data sets. Use this function in place of a table of critical values for the t-distribution.
Syntax
T.DIST.RT(x,deg_freedom)
The T.DIST.RT function syntax has the following arguments:
• X Required. The numeric value at which to evaluate the distribution.
• Deg_freedom Required. An integer indicating the number of degrees of freedom.

----------------------------------------------------------------------------------------------------------------

2.

μd = μ2−μ1

Sample Mean of the differences :	1.5
Sample Standard Deviation of the differences : sd	27.2
Sample Size : n	124
Level of significance :	0.002
/2	0.001
Degrees of Freedom : n-1	123

For two tailed test, Critical values :

for n-1 degrees of freedom;

i.e

for 123 degrees of freeedom

Critical values : ± 3.1578

Test Statistic = 0.6141