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.

i believe the correct answer is option 4.principalities were small territories that were run by russian rulers.

which statement correctly defines principalities in northern asia in the 1200s? principalities were small territories that were run by russian rulers.

hope i could ! : )