The Student's t distribution table gives critical values for the Student's t distribution. Use an appropriate d.f. as the row header. For a right-tailed test, the column header is the value of a found...

Extracted text: The Student's t distribution table gives critical values for the Student's t distribution. Use an appropriate d.f. as the row header. For a right-tailed test, the column header is the value of a found in the one-tail area row. For a left-tailed test, the column header is the value of a found in the one-tail area row, but you must change the sign of the critical value t to -t. For a two-tailed test, the column header is the value of a from the two-tail area row. The critical values are the t values shown. A random sample of 41 adult coyotes in a region of northern Minnesota showed the average age to be x = 2.13 years, with sample standard deviation s = 0.83 years. However, it is thought that the overall population mean age of coyotes is u = 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 a = 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. O Fail to reject the null hypothesis, there is insufficient evidence that the average age of Minnesota coyotes is higher than 1.75 years. O Fail to reject the null hypothesis, there is sufficient evidence that the average age of Minnesota coyotes is higher than 1.75 years. O Reject the null hypothesis, there is insufficient evidence that the average age of Minnesota coyotes is higher than 1.75 years. O Reject the null hypothesis, there is sufficient evidence that the average age of Minnesota coyotes is higher than 1.75 years. Compare your conclusion with the conclusion obtained by using the P-value method. Are they the same? O The conclusions obtained by using both methods are the same. O we reject the nll hypothesis using the P-value method, but fail to reject using the traditional method. O we reject the null hypothesis using the traditional method, but fail to reject using the P-value method.