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Math 308 Spring 2009
Study Sheet and Sample Problems for Test 3
Text for TEST 3 Assigned Other material 7.1 Point estimation 5 7.2 Interval estimation
Hypothesis testing: Understand the hypothesis-testing five-step process. Know the hypotheses for tests about one mean, two means and more than two means. Know which test statistics to use based on the assumptions of the test statistic. Know how to relate the alternate hypothesis to the decision rule (rejection region). Know how to calculate the test statistic from a formula sheet. 7.3 Tests of Hypotheses Assigned Class Handout: Statistical Testing 7.4 Null hypotheses and tests of hypotheses
Class Handout: Statistical Testing 7.5 Hypotheses about one mean 7.39, 7.43, 7.48 Class Handout: Statistical Testing 7.8 Inference concerning the difference between two means 7.68, 72 Class Handout: Statistical Testing 9.1-9.3 4, 11, 22, 27 12.1,12.2 ANOVA: One-way ANOVA (Completely randomized design) Example on Handout Online class notes: Analysis of Variance 11.1-11. Simple Linear Regression Example on Handout Online class notes: Regression
20.00 30.00 40.00 50. MotoCars 0 2 4 6 8 Frequency Mean = 36. Std. Dev. = 6. N = 20 Old Test Questions
- A random sample of the number of MotoCars made at the Electric MotoCar Factory yielded the numbers in the table. The graph is a histogram of the number of MotoCars made for the twenty randomly chosen days. The mean daily number of cars was 36.75 and the standard deviation was 6.71115. The owners of Electric MotoCar want to know whether the actual (population) mean is greater than 34 cars/day. Fill in the five steps of the hypothesis-testing process for testing this hypothesis. Use a significance level of 0.05. (a) Hypotheses[3 points]: (b) Significance level and test statistic (give your reasons for choosing the test statistic) [7]: (Question 1 continued) (c) Decision rule (rejection region) 4]: (d) Computed sample statistic [8]: (e) Decision (include reason for decision)[2]:
- [8] Refer to problem 1. What is the probability of a Type II error if ^ 35. MotoCars daily?
- [10] Refer again to problem 1. Give the 95% confidence interval for the actual number of MotoCars produced daily. MotoCars 36. 28. 49. 44. 35. 37. 36. 35. 37. 36. 33. 39. 40. 32. 31. 41. 42. 30. 23. 51.
corresponding to the four Treatments. Number your steps and use problem 1 as a general reference for an appropriate answer. Treatment 1 Treatment 2 Treatment 3 Treatment 4 6 13 7 3 4 10 9 6 5 13 11 1 12 4 1 Complete the following table as part of your answer. Source Sum of Squares Degrees of freedom Mean Square F Treatment Error OTHER SAMPLE PROBLEMS FOR TEST 3: 1. The following figures are the number of widgets filled per day at two competing plants. Plant A Plant B 19 23 17 19 21 21 15 15 15 17 12 11 17 12 12 10 24 16 16 20 12 15 15 12 19 20 11 13 14 18 13 17 20 14 14 16 18 22 21 18 Mean = 17.85 Mean = 14. Std Dev = 3.50 Std Dev = 3. With the information you have been given so far, how would you verify that each sample is from a normal population. How would you find the probability of a sample mean of 17.85 or larger for Plant A if you assume that the actual mean for Plant A is 15?
- A cola dispensing machine at XYZ company dispenses 9 ounce cups of cola. An employee of XYZ thinks that the machine is cheating consumers. A random sample of 50 cups has a mean of 8.7 ounces and a standard deviation of 0.5 ounces. If the mean volume of cola dispensed is actually 9 ounces, what is the probability of a mean this small or smaller?
- The functional reach of adult men is a normally distributed random variable with mean 32.33 inches and standard deviation 1.63 inches.
(a) What is the probability that the reach of a randomly selected man exceeds 34.5 inches? (b) A second man is randomly selected. What is the probability that both men have reaches exceeding 34.5 inches? (Assume independence.) (c) What is the probability that the reach of a randomly selected man is between 31.515 inches and 33.96 inches?
- The Leakey Brothers offer a one-year warranty on radiator replacements. The time to failure of a Leakey radiator has an exponential distribution with mean process rate λ= 0.6 per year. (a) What is the probability of a radiator failing within the warranty period? (b) If the Leakey Brothers make a profit of $125 on every radiator that survives the warranty period and lose $50 on each radiator that fails under warranty, what is the expected profit per radiator sold? Some sample questions for Test 3: Note that there is no ANOVA question.
- The following figures are the number of widgets produced per day at two competing plants. Plant A Plant B 19 23 17 19 21 21 15 15 15 17 12 11 17 12 12 10 24 16 16 20 12 15 15 12 19 20 11 13 14 18 13 17 20 14 14 16 18 22 21 18 Mean = 17.85 Mean = 14. Std Dev = 3.50 Std Dev = 3. A. With the information you have been given so far, how would you verify that each sample is from a normal population. Why is this “check” important? B. Find the 95% CI for the mean of the number of widgets made daily by Plant A. C. Test the hypothesis that Plant A makes more widgets daily than Plant B.
