Question

Review how to compare two distributions. Solve for the 95 CI of each of the following and indicate whether the two distributions are significantly different with F-test and t-test. Assume the values are:

Group 1: 22, 24, 23, 27, 28

Group 2: 23, 25, 26, 25, 28

Answer 1

Using MS-Excel

Hypothesis

By using F test

F-Test Two-Sample for Variances
	Variable 1	Variable 2
Mean	24.8	25.4
Variance	6.7	3.3
Observations	5	5
df	4	4
F	2.030303
P(F<=f) one-tail	0.254826
F Critical one-tail	6.388233

p valus is 0.2548>0.05 so we accept null hypothesis

so we say that group 1 and group 2 are equal mean there is no difference between two groups

By using T test

t-Test: Two-Sample Assuming Unequal Variances
	Variable 1	Variable 2
Mean	24.8	25.4
Variance	6.7	3.3
Observations	5	5
Hypothesized Mean Difference	0
df	7
t Stat	-0.42426
P(T<=t) one-tail	0.342054
t Critical one-tail	1.894579
P(T<=t) two-tail	0.684108
t Critical two-tail	2.364624

p valus is 0.6841>0.05 so we accept null hypothesis

so we say that group 1 and group 2 are equal mean there is no difference between two groups

Also we saw the p value of using f test and T test are equal they are not differ

2) 95% confidence interval

sqrt(n)

for group 1:

=24.81.96*2.5884/sqrt(5)

=24.82.2689

for group 2:

=25.41.96*(1.8165)/sqrt(5)

=25.41.5922