To perform a test of the null and alternative hypotheses shown below, random sam
ID: 1210962 • Letter: T
Question
To perform a test of the null and alternative hypotheses shown below, random samples were selected from the two normally distributed populations with equal variances. The data are shown below. Test the null hypothesis using an alpha level equal to 0.10.
Sample from Population 1: 33,43,27,36,37,34,26,39,42,39
Sample from Population 2: 45,53,37,47,41,38,41,47,48,43
H0: 1 2 = 0
HA: 1 – 0
Determine the rejection region for the test statistic t. Select the correct choice below and fill in the answer box(es) to complete your choice.
A. t < ____ or t > ____
B. t > ___
C. t < ___
Calculate the value of the test statistic. t = ___
Since the test statistic ____ (is not, or is) in the rejection region, _____ (reject, or do not reject) the null hypothesis. There is ____ (sufficient, or insufficient) evidence to conclude that the two population means are different.
Explanation / Answer
First step is to represent our scientific question is the null and alternative
hypothesis.
The null: Ho: m1-m2 = 0 represents the condition that the populations are centered
in the same spot.
As with one-sample and matched pairs hypothesis testing we can have a one-sided
or two-sided alternative.
The two sided alternative is that the means differ. That is m1-m2 does not equal
zero.
It is two sample problem with 1 and 2 not equal
So we use t test for the same
So for that we have to find out Xbar and S for both data
X1 bar = 35.6 X2 bar = 44
And s1= 5.74 and s2 = 4.94
T= -6.926
Paired Samples Statistics
Mean
N
Std. Deviation
Std. Error Mean
Pair 1
one
35.60
10
5.739
1.815
two
44.00
10
4.944
1.563
Paired Samples Test
Paired Differences
Mean
Std. Deviation
Std. Error Mean
95% Confidence Interval of the Difference
Lower
Upper
Pair 1
one - two
-8.400
3.836
1.213
-11.144
-5.656
Paired Samples Test
t
df
Sig. (2-tailed)
Pair 1
one - two
-6.926
9
.000
Paired Samples Statistics
Mean
N
Std. Deviation
Std. Error Mean
Pair 1
one
35.60
10
5.739
1.815
two
44.00
10
4.944
1.563
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