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# OPER 3360 SECTION 003 Fall 2012 TAKE-HOME EXAM #3 NAME: SUBMISSION INSTRUCTIONS: Due Date: MIDNIGHT, Tuesday, December 18, 2012 2. Print out this...

NAME: -2- . 1. (20 Points) Bastien, Inc. has been manufacturing small automobiles that have averaged 50 miles per gallon of gasoline in highway driving. The company has developed a more efficient engine for its small cars and now advertises that its new small cars average more than 50 miles per gallon in highway driving. An independent testing service road-tested 36 of the automobiles. The sample showed an average of 51.5 miles per gallon. The population standard deviation is 6 miles per gallon. a. State the null and alternate hypotheses for testing the stated claim. b. Test the stated claim for = 0.04. c. Interpret the result of the hypothesis test regarding the stated claim. d. What is the p-value associated with this hypothesis test? e. Create a 96% confidence interval for the average miles per gallon in highway driving. f. Does the confidence interval created include the hypothesized value? 2. (15 Points) A lathe is set to cut bars of steel into lengths of 6 centimeters. The lathe is considered to be in perfect adjustment if the average length of the bars it cuts is 6 centimeters. A sample of 121 bars is selected randomly and measured. It is determined that the average length of the bars in the sample is 6.08 centimeters. The sample standard deviation is 0.44 centimeters. Determine whether or not the lathe is in perfect adjustment. Use a .05 level of significance. 3. (20 Points) Information regarding the ACT scores of students in four different majors are given in the table below. Determine if there is a significant difference in the means of ACT score between the different majors. Use a 0.06 level of significance. Management Marketing Finance Accounting 27 21 28 28 26 28 25 23 23 25 26 26 21 21 26 22 28 26 24 24 26 24 23 28 23 25 26 26 25 21 30 28 22 27 26 25 23 21 24 30 29 22 23 26 4. (15 Points) In a completely randomized experimental design, 8 experimental units were used for the first treatment, 12 experimental units for the second treatment, and 13 experimental units for the third treatment. The Mean Square Error equals 5 and the F test statistic equals 5.5. a. Create the ANOVA table for this experiment. b. Using a 0.05 level of significance, is there a significant difference among the means?
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