Part One: You wish to test the following claim (HaHa) at a
significance level of α=0.001α=0.001.
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=11n1=11 with a mean of
M1=76.2M1=76.2 and a standard deviation of SD1=8.7SD1=8.7 from the
first population. You obtain a sample of size n2=24n2=24 with a
mean of M2=95.3M2=95.3 and a standard deviation of SD2=18.2SD2=18.2
from the second population.
What is the test statistic for this sample? (Report answer accurate
to three decimal places.)
test statistic =
What is the p-value for this sample? (Report answer accurate to
four decimal places.)
p-value =
The p-value is...
This test statistic leads to a decision to...
As such, the final conclusion is that...
Part Two: You wish to test the following claim (HaHa) at a
significance level of α=0.02α=0.02. For the context of this
problem, d=x2−x1d=x2-x1 where the first data set represents a
pre-test and the second data set represents a post-test.
Ho:μd=0Ho:μd=0
Ha:μd≠0Ha:μd≠0
You believe the population of difference scores is normally
distributed, but you do not know the standard deviation. You obtain
the following sample of data:
pre-test | post-test |
---|---|
49.9 | 40.4 |
62.2 | 35.7 |
23.4 | 7.7 |
45.2 | 43.3 |
46.8 | 36.6 |
28.9 | 9.2 |
What is the critical value for this test? (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...
This test statistic leads to a decision to...
As such, the final conclusion is that...
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