In tests of significance about an unknown parameter,what does the test statistic represent?

A) The value of the unknown parameter under the null hypothesis
B) The value of the unknown parameter under the alternative hypothesis
C) A measure of compatibility between the null and alternative hypotheses
D) A measure of compatibility between the null hypothesis and the data

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katie hathaway · Accepted Answer

Final Answer : D, Explanation :  The test statistic represents a measure of compatibility between the null hypothesis and the data, by providing a numerical summary of how well the observed data align with the null hypothesis. It allows us to quantify the degree of deviation between what we expect under the null hypothesis and what we actually observe in the sample. Choosing option A or B as the answer would imply that the test statistic directly represents the value of the unknown parameter, which is incorrect. Option C is also incorrect because the test statistic is not a measure of compatibility between the null and alternative hypotheses, but rather between the null hypothesis and the observed data.

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