statistics question

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 51 adult coyotes in a region of northern Minnesota showed the average age to be x = 2.05 years, with sample standard deviation s = 0.75 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	=

Answer 1

test statistic t = (sample mean - population mean)/(sample standard deviation/sample size**0.5)

= (2.05 - 1.75)/(0.75/51**0.5) = 2.857

critical region. because asking if sample data shows Minnesota coyotes live longer than 1.75 years, this is a right tail test with alpha = 0.01 and 51-1 = 50 degrees of freedom. critical t value for right tail test is 2.403.

since test statistic t > 2.403, we can reject the null hypothesis and conclude there is sufficient evidence that Minnesota coyotes live longer than 1.75 years.