Question

Consider the following set of random measurements, taken from a normally distributed population before and after a treatment was applied.

Before Treatment	[7.38, 6.21, 7.9, 6.46, 7.56, 7.92]
After Treatment	[5.89, 6.54, 6.27, 6.52, 7.18, 6.98]
Difference	[1.49, -.33, 1.63, -.6E-1, .38, .94]

Test the null hypothesis H0:μD=0against the alternative hypothesis HA:μD≠0.

a) What is the value of the t test statistic? Remember to run a T test on just he difference list. Round your response to at least 3 decimal places.

b) What is the range in which the P-value falls?

A		P-value > 0.10
B		0.05 < P-value < 0.10
C		0.025 < P-value < 0.05
D		0.010 < P-value < 0.025
E		P-value < 0.010

Is the null hypothesis rejected at:

a) the .05 level of significance? Yes or No

b) the .10 level of significance? Yes or No

Answer 1

a)

Before    after   dbar
7.38   5.89   1.49
6.21   6.54   -0.33
7.9   6.27   1.63
6.46   6.52   -0.06
7.56   7.18   0.38
7.92   6.98   0.94

dbar = μ(before) - μ(after) = 0.675
s(dbar)= 0.8104

SE = s(dbar)/sqrt(n)
= 0.8104/sqrt(6)
= 0.3308

Test Statisitcs,
t = dbar/SE  
= 0.675/0.3308
= 2.040

b)

p value = 0.0969

0.05 < P-value < 0.10

Is the null hypothesis rejected at:

a) the .05 level of significance No

b) the .10 level of significance Yes