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?

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

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

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

.

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 .

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

A similar problem is given at link

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.

the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).

mr. india