Question

7. The large tankers that transport oil from the U.S. gulf coast to Canadian refineries typically carry between 800,000 and 1.3 million barrels of product. In order to control the production of refined petroleum, Canadian refineries need to minimize the variation in arrival times of large tankers or their refineries may have too little product on hand. The industry typically views a standard deviation of 9.3 days as acceptable given the influence of weather, labor cost, and mechanical failures cannot be controlled. A random sample of delivery times was collected for 35 tankers over the past year. The voyage duration (in days) is shown below. Does this data demonstrate the standard deviation over the past year is acceptable at a 5% significance level?

45 40 49 49 30 54 28 45 61 58 41 37 36 17 42 35 56 34 64 67 23 44 24 46 51 58 36 44 54 41 55 24 54 40 36

a. Give the null and alternative hypotheses for this test in symbolic form.

H0:

H1:

b. Determine the value of the test statistic.

c. Determine the appropriate critical value(s). d Determine the P-value.

e. Based upon your work above, should you "Reject the null hypothesis" or "Fail to reject the null hypothesis?" Explain your reasoning.

f. Is there sufficient statistical evidence to support the claim that the standard deviation of voyage duration is at an industry accepted value? Explain your reasoning.

Answer 1

From the given data : Sample size=n=35

Sample standard deviation= s =

Significance level =

a. Hypothesis : Vs

b. The value of the test statistic is ,

c. Critical values : ; From excel "=CHIINV(0.025,34)"

and ; From excel "=CHIINV(0.975,34)"

P-value = ; From excel "=CHIDIST(59.7058,34)"

e. Decision : Here , the value of the test statistic lies in the rejection region

Also , P-value = 0.0042 <

Therefore , reject the null hypothesis

f. Conclusion : Hence , there is not sufficient statistical evidence to support the claim that the standard deviation of voyage duration is at an industry accepted value.