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. We wish to compare the means of two populations using paired observations. Suppose that d overbar equals3.125, subscript dequals2.911, and nequals8, and that you wish to test the following hypothesis at the 10% level of significance. H0: mu Subscript d equals 0 against H1: muSubscript dgreater than0 What decision rule would you use?

We can use the p value as a decision rule is we reject the null hypothesis.

Now we can find the degrees of freedom given by:

And the p value would be:

And since the we have enough evidence to reject the null hypothesis in favor to the alternative hypothesis.

Step-by-step explanation:

For this case we have the following statistics for the difference between the paired observations:

the sample mean for the paired difference

the sample deviation for the paired difference data

the sample size

The system of hypothesis that we want to check is:

Null hypothesis:

Alternative hypothesis:

And the statistic is given by:

And replacing we got:

We can use the p value as a decision rule is we reject the null hypothesis.

Now we can find the degrees of freedom given by:

And the p value would be:

And since the we have enough evidence to reject the null hypothesis in favor to the alternative hypothesis.

step-by-step explanation:

if you meant, "on the way from (3, 2) to (3, 14):

x does not change; y increases by 12.

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