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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?

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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 ago
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