Question

You wish to test the following claim (Ha) at a significance
level of α=0.001

Ho:μ1=μ2

Ha:μ1≠μ2

You believe both populations are normally distributed, but you do
not know the standard deviations for either. Use non-pooled test.
You obtain a sample of size n1=17 with a mean of M1=51.4 and a
standard deviation of SD1=16.2 from the first population. You
obtain a sample of size n2=23 with a mean of M2=65.4 and a standard
deviation of SD2=18.4 from the second population.

What is the critical value for this test? For this calculation, use
the conservative under-estimate for the degrees of freedom as
mentioned in the textbook. (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 =

The test statistic is...

- in the critical region
- not in the critical region

This test statistic leads to a decision to...

- reject the null
- accept the null
- fail to reject the null

As such, the final conclusion is that...

- There is sufficient evidence to warrant rejection of the claim that the first population mean is not equal to the second population mean.
- There is not sufficient evidence to warrant rejection of the claim that the first population mean is not equal to the second population mean.
- The sample data support the claim that the first population mean is not equal to the second population mean.
- There is not sufficient sample evidence to support the claim that the first population mean is not equal to the second population mean.

Answer #1

You wish to test the following claim (HaHa) at a significance
level of α=0.01α=0.01.
Ho:μ1=μ2Ho:μ1=μ2
Ha:μ1≠μ2Ha:μ1≠μ2
You believe both populations are normally distributed, but you do
not know the standard deviations for either. However, you also have
no reason to believe the variances of the two populations are not
equal. You obtain a sample of size n1=15n1=15 with a mean of
M1=76.2M1=76.2 and a standard deviation of SD1=12.6SD1=12.6 from
the first population. You obtain a sample of size n2=18n2=18 with...

You wish to test the following claim (H1) at a significance
level of α=0.01
Ho:μ1=μ2
H1:μ1>μ2
You believe both populations are normally distributed, but you do
not know the standard deviations for either. However, you also have
no reason to believe the variances of the two populations are not
equal. You obtain a sample of size n1=20 with a mean of M1=84.6 and
a standard deviation of SD1=18.1 from the first population. You
obtain a sample of size n2=21 with...

You wish to test the following claim (HaHa) at a significance
level of α=0.02α=0.02.
Ho:μ1=μ2Ho:μ1=μ2
Ha:μ1<μ2Ha:μ1<μ2
You believe both populations are normally distributed, but you do
not know the standard deviations for either. Use non-pooled test.
You obtain a sample of size n1=25n1=25 with a mean of
M1=55.8M1=55.8 and a standard deviation of SD1=18.5SD1=18.5 from
the first population. You obtain a sample of size n2=26n2=26 with a
mean of M2=65.5M2=65.5 and a standard deviation of SD2=6.7SD2=6.7
from the second population....

You wish to test the following claim (H1H1) at a significance
level of α=0.005α=0.005.
Ho:μ1=μ2Ho:μ1=μ2
H1:μ1≠μ2H1:μ1≠μ2
You obtain a sample of size n1=83n1=83 with a mean of
M1=74.6M1=74.6 and a standard deviation of SD1=10.4SD1=10.4 from
the first population. You obtain a sample of size n2=75n2=75 with a
mean of M2=72.3M2=72.3 and a standard deviation of SD2=9.1SD2=9.1
from the second population.
What is the critical value for this test? (Report answer accurate
to three decimal places.)
critical value = ±±
What...

You wish to test the following claim (HaHa) at a significance
level of α=0.001
Ho:μ1=μ2
Ha:μ1≠μ2
You believe both populations are normally distributed, but you
do not know the standard deviations for either. And you have no
reason to believe the variances of the two populations are equal
You obtain a sample of size n1=13 with a mean of ¯x1=69.1 and a
standard deviation of s1=15.5 from the first population. You obtain
a sample of size n2=22 with a mean...

You wish to test the following claim (H1H1) at a significance
level of α=0.002α=0.002.
Ho:μ1=μ2Ho:μ1=μ2
H1:μ1<μ2H1:μ1<μ2
You believe both populations are normally distributed, but you do
not know the standard deviations for either. However, you also have
no reason to believe the variances of the two populations are not
equal. You obtain a sample of size n1=14n1=14 with a mean of
M1=71.4M1=71.4 and a standard deviation of SD1=7.5SD1=7.5 from the
first population. You obtain a sample of size n2=12n2=12 with...

You wish to test the following claim (Ha) at a significance
level of α=0.01 . Ho:μ1=μ2 Ha:μ1≠μ2 You believe both populations
are normally distributed, but you do not know the standard
deviations for either. And you have no reason to believe the
variances of the two populations are equal You obtain a sample of
size n1=21 with a mean of ¯x1=65.4 and a standard deviation of
s1=8.8 from the first population. You obtain a sample of size n2=17
with a...

You wish to test the following claim (HaHa) at a significance
level of α=0.002α=0.002.
Ho:μ1=μ2
Ha:μ1<μ2
You believe both populations are normally distributed, but you do
not know the standard deviations for either. However, you also have
no reason to believe the variances of the two populations are not
equal. You obtain the following two samples of data.
Sample #1
Sample #2
87.5
100.8
78.3
62.9
108.3
76.4
100.8
73.4
61.8
84.5
83.5
77.2
84.2
87.1
71
81.7
66.9
67.5...

You wish to test the following claim (H1H1) at a significance
level of α=0.001α=0.001.
Ho:μ1=μ2Ho:μ1=μ2
H1:μ1>μ2H1:μ1>μ2
You believe both populations are normally distributed, but you do
not know the standard deviations for either. However, you also have
no reason to believe the variances of the two populations are not
equal. You obtain a sample of size n1=24n1=24 with a mean of
M1=68.9M1=68.9 and a standard deviation of SD1=8.6SD1=8.6 from the
first population. You obtain a sample of size n2=24n2=24 with...

You wish to test the following claim (Ha) at a significance
level of α=0.05.
Ho:μ1=μ2
Ha:μ1<μ2
You believe both populations are normally distributed, but you
do not know the standard deviations for either. And you have no
reason to believe the variances of the two populations are equal
You obtain a sample of size n1=28 with a mean of ¯x1=67.6 and a
standard deviation of s1=10.7 from the first population. You obtain
a sample of size n2=24 with a mean...

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