Question

Determine the decision criterion for rejecting the null hypothesis in the given hypothesis​ test; i.e., describe the values of the test statistic that would result in rejection of the null hypothesis. Suppose you wish to test the claim that mu Subscript dμd​, the mean value of the differences d for a population of paired​ data, is greater than 0. Given a sample of n equals=15 and a significance level of alphaαequals=​0.01, what criterion would be used for rejecting the null​ hypothesis

Answer 1

Explanation:

Hello!

Given the statistical hypothesis:

H₀:μd≤0

H₁: μd>0

and the significance level:

α:0.01

With the sample size 15 and assuming all conditions are met, the most accurate statistic to use will be a Student's t

t= (x[bar]d-μd)/(Sd/√n)~tₙ₋₁

This is a one-tailed test, you have two options. You either calculate the p-value for the test and compare it to the level of significance.

If p-value > than α then you support the null hypothesis.

If p-value ≤ than α then you reject the null hypothesis.

Or you calculate the observed t value and compare it with a critical value, in this case, tₙ₋₁;₋ₐ. The critical region is one-tailed to the right, so you'll reject the null hypothesis if the calculated t value is equal or greater than the critical value and you will support the null hypothesis if the calculated t-value is less than the critical value.

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