Question
In: Statistics and Probability
How can you reach a hypothesis-testing conclusion by examining a confidence interval for a two independent...
How can you reach a hypothesis-testing conclusion by examining a confidence interval for a two independent sample t-test? Is it possible? If so, how?
Solutions
Expert Solution
Yes, it is possible to reach a hypothesis-testing conclusion by examining a confidence interval for a two independent sample t-test.
Suppose we are interested to test if there is any significant difference in the means of two independent samples and our test statistic is the difference of sample means.
Let the significance level of the test is 
, 0<<1
and (1-)100%
confidence interval is (t1, t2). That means
if we take the sample 100 times and test the difference in means,
(1-)100
times this interval will be able to contain the difference between
two population means and
100 times this interval is expected to fail to contain the true
difference in means.
Our Null hypothesis: true difference is 0 and alternative hypothesis: true difference is not 0.
If our test statistic value falls outside the confidence
interval, then we will reject the null hypothesis at 100%
level of significance. If it falls inside the confidence interval
then we fail to reject null hyothesis at 100%
level of significance.
orchestra answered 2 years agoRelated Solutions
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The following are a few problems on hypothesis testing. The
corresponding confidence interval
(CI) question is also asked. This is a good practice for students
to see how hypothesis testing
results reflect in the confidence interval estimates. In the first
problem, the steps are given to get
the hypothesis testing results and the CI estimates. It is a good
practice to follow the steps. Try to
use the same steps in the subsequent problems.
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The following are a few problems on hypothesis testing. The corresponding confidence interval (CI) question is...
The following are a few problems on hypothesis testing. The
corresponding confidence interval
(CI) question is also asked. This is a good practice for students
to see how hypothesis testing
results reflect in the confidence interval estimates. In the first
problem, the steps are given to get
the hypothesis testing results and the CI estimates. It is a good
practice to follow the steps. Try to
use the same steps in the subsequent problems.
1. The life span of 100...
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Test the hypothesis that the average table time exceeds 98
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county and 8 farms from in Yellow County. Can it be concluded at
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Develop a 90% confidence interval for this random sample and
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Test the hypothesis that the average table time exceeds 98
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