Question

Use the information provided to answer the questions.
Population 1= 11   3   9   4      
Population 2= 13   7   7   9   6   5

Calculate the pooled estimate of σ2, the associated degrees of freedom, and the observed value of the t statistic. (Round s2 and your t statistic to three decimal places.)

S(squared) =

df =

t =

What is the rejection region using α = 0.05? (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.)

t > __________

t < __________

Answer 1

using excel>Addin>phstat>two sample test

we have

Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference	0
Level of Significance	0.05
Population 1 Sample
Sample Size	4
Sample Mean	6.75
Sample Standard Deviation	3.862210075
Population 2 Sample
Sample Size	6
Sample Mean	7.833333333
Sample Standard Deviation	2.857738033
Intermediate Calculations
Population 1 Sample Degrees of Freedom	3
Population 2 Sample Degrees of Freedom	5
Total Degrees of Freedom	8
Pooled Variance	10.6979
Standard Error	2.1113
Difference in Sample Means	-1.0833
t Test Statistic	-0.5131
Two-Tail Test
Lower Critical Value	-2.3060
Upper Critical Value	2.3060
p-Value	0.6217
Do not reject the null hypothesis

from output

S(squared) =10.698

df =8

t = -0.513

the rejection region using α = 0.05 is

t >2.306

t < -2.306