Question

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 α found in the one-tail area row. For a left-tailed test, the column header is the value of α 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 α 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 = 2.09 years, with sample standard deviation s = 0.81 years. However, it is thought that the overall population mean age of coyotes is μ = 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 α = 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. Reject the null hypothesis, there is insufficient evidence that the average age of Minnesota coyotes is higher than 1.75 years. Reject the null hypothesis, there is sufficient evidence that the average age of Minnesota coyotes is higher than 1.75 years. Fail to reject the null hypothesis, there is insufficient evidence that the average age of Minnesota coyotes is higher than 1.75 years. Fail to 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? We reject the null hypothesis using the traditional method, but fail to reject using the P-value method. We reject the null hypothesis using the P-value method, but fail to reject using the traditional method. The conclusions obtained by using both methods are the same.

Answer 1

Given a random sample of n = 41 adult coyotes in a region of northern Minnesota showed the average age to be = 2.09 years, with sample standard deviation s = 0.81 years.

However, it is thought that the overall population mean age of coyotes is μ = 1.75 and the significance level is α = 0.01.

Thus based on the claim the hypotheses are:

Based on the hypothesis it will be a right-tailed test, but the sample size is greater than 30 and the population standard deviation is unknown hence t-distribution is applicable for hypothesis testing, hence degree of freedom will be used which is calculated as df = n-1= 41- 1= 40.

Critical value method for hypothesis testing

Test statistic:

Rejection region:

Based on the type of hypothesis and given significance level the critical score for the rejection region is calculated using the excel formula for t-distribution which is =T.INV(1-0.01, 40), thus the tc is computed as 2.423.

Hence reject the Ho if t > tc.

Conclusion:

Since the test statistic is greater than the critical score hence the conclusion is:

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

P-value method

Reject Ho if P-value is less than 0.01.

P-value:

The P-value is calculated using the excel formula for t-distribution which is =T.DIST.RT(2.688, 40), thus the P-value is computed as 0.0052.

Conclusion:

Since the P-value is less than 0.01 hence The conclusions obtained by using both methods are the same.

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