Question

TRACTOR SKIDDING HYPOTHESIS TESTING Forest engineers are interested in studying the skidding distances of tractors along a new road in a European Forest. The engineers collect data on a random sample of 12 tractors. The collected data (in meters) are: 350, 285, 574, 439, 295, 184, 261, 273, 400, 311, 141, 425. The average skidding distance for the sample of 12 tractors is 328.17 and the standard deviation is 118.46. Local loggers working on the road believe that the mean skidding distance of all tractors on this road is 325 meters. The engineers believe it is much greater than this. Conduct a hypothesis test based on the engineer’s belief. Conduct this hypothesis test at a significance level of .01. Which is the correct rejection region? Enter 1,2,3, or 4 in the box. All values of T greater than the critical value. All values of Z greater than the critical value. All values of T less than the critical value. All values of Z less than the critical value.

Answer 1

Since n < 12 and standard deviation is unknown, we use the students t test.

The test is a right tailed test, hence the rejection region is (1) All values of t greater than the critical value.

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Given = 325, = 328.17, s = 118.46, n = 12

The Hypothesis:

H0: = 325

Ha: > 325

This is a right tailed Test.

The Test Statistic: Since the population standard deviation is unknown, we use the students t test.

The test statistic is given by the equation:

The p Value:    The p value (Right Tail) for t = 0.09, for degrees of freedom (df) = n-1 = 11, is; p value = 0.465

The Critical Value:   The critical value (Right Tail) at = 0.01, for df = 11, tcritical = +2.718

The Decision Rule:   If tobserved is > tcritical, then Reject H0

Also if P value is < , Then Reject H0.

The Decision:   Since tobserved (0.09) is < tcritical (2.718), We Fail to Reject H0.

Also since P value (0.465) is > (0.01) , We Fail to Reject H0.

The Conclusion: There isn't sufficient evidence at the 99% significance level to conclude that the skidding distance of tractors is greater than 325 meters.