TheStudent'stdistribution tablegives critical values for the Student'stdistribution. Use an appropriated.f.as the row header. For aright-tailedtest, the column header is the value offound in theone-tail arearow. For aleft-tailedtest, the column header is the value offound in theone-tail arearow, but you must change the sign of the critical valuettot. For atwo-tailedtest, the column header is the value offrom thetwo-tail arearow. The critical values are thetvalues shown.

A random sample of51adult coyotes in a region of northern Minnesota showed the average age to bex=2.13years, with sample standard deviations=0.81years. However, it is thought that the overall population mean age of coyotes is= 1.75.Do the sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years? Use= 0.01.Solve the problem using the critical region method of testing (i.e., traditional method). (Round your answers to three decimal places.)

test statistic=

critical value=

State your conclusion in the context of the application.

a. Fail to reject the null hypothesis, there is insufficient evidence that the average age of Minnesota coyotes is higher than 1.75 years.

b. Fail to reject the null hypothesis, there is sufficient evidence that the average age of Minnesota coyotes is higher than 1.75 years.

c. Reject the null hypothesis, there is sufficient evidence that the average age of Minnesota coyotes is higher than 1.75 years.

d. Reject the null hypothesis, there is insufficient evidence that the average age of Minnesota coyotes is higher than 1.75 years.

Compare your conclusion with the conclusion obtained by using theP-value method. Are they the same?

a. We reject the null hypothesis using the traditional method, but fail to reject using theP-value method.

b. The conclusions obtained by using both methods are the same.

c. We reject the null hypothesis using theP-value method, but fail to reject using the traditional method.