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.

y=mx+b is the final answer!   : )

7! = 7×6×5×4×3×2

3! = 3× 2

as 7! is multiple of 3! because 7! contains 3! that is 3× 2 as factor

so 7! /(3! ) = 7× 6× 5× 4

= 42 × 20

= 840

its b) 840✌✌✌

dhruv⭐