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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 ​, the mean value of the differences d for a population of paired​ data, is greater than 0. Given a sample of n15 and a significance level of ​0.01, what criterion would be used for rejecting the null​ hypothesis?

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ogorwyne

Answer:

reject null hypothesis if calculated t value > 2.624

Step-by-step explanation:

n = 15

To calculate degree of freedom, n -1 = 14

The claim says ud>0

The decision rule would be to reject this null hypothesis if the test statistics turns out to be greater than the critical value.

With df =14

Confidence level = 0.01

Critical value = 2.624 (for a one tailed test)

If the t value calculated is > 2.624, we reject null hypothesis.

Using the t-distribution and it's critical values, the decision rule is:

  • t < 2.624: Do not reject the null hypothesis.
  • t > 2.624: Reject the null hypothesis.

At the null hypothesis, we test if the mean is not greater than 0, that is:

[tex]H_0: \mu \leq 0[/tex]

At the alternative hypothesis, we test if the mean is greater than 0, that is:

[tex]H_1: \mu > 0[/tex].

We then have to find the critical value for a right-tailed test(test if the mean is more than a value), with 15 - 1 = 14 df and a significance level of 0.01. Using a t-distribution calculator, it is [tex]t^{\ast} = 2.624[/tex].

Hence, the decision rule is, according to the test statistic t:

  • t < 2.624: Do not reject the null hypothesis.
  • t > 2.624: Reject the null hypothesis.

A similar problem is given at https://brainly.com/question/13949450