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 46 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 =

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis: μ = 1.75
Alternative Hypothesis: μ > 1.75

Rejection Region
This is right tailed test, for α = 0.01 and df = 45
Critical value of t is 2.412.
Hence reject H0 if t > 2.412

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (2.09 - 1.75)/(0.81/sqrt(46))
t = 2.847

P-value Approach
P-value = 0.003
As P-value < 0.01, reject the null hypothesis.