MATH 302 FINAL EXAM 1 – QUESTION AND ANSWERS

MATH 302 Final Exam – Question and Answers PART 1 OF 16 A company operates four machines during three shifts each day. From production records, the data in the table below were collected. At the .05 level of significance test to determine if the number of breakdowns is independent of the shift. The chi-square goodness-of-fit test can be used to test for: PART 2 OF 16 In a simple linear regression analysis, the following sum of squares are produced: ____________ is/are especially helpful in identifying outliers. The marketing manager of a large supermarket chain would like to use shelf space to predict the sales of pet food. For a random sample of 12 similar stores, she gathered the following information regarding the shelf space, in feet, devoted to pet food, and the weekly sales in hundreds of dollars. PART 3 OF 16 Which of the following statements is true regarding the F – distribution? Multiple myeloma or blood plasma cancer is characterized by increased blood vessel formulation in the bone marrow that is a prognostic factor in survival. One treatment approach used for multiple myeloma is stem cell transplantation with the patient’s own stem cells. The following data represent the bone marrow microvessel density for a sample of 7 patients who had a complete response to a stem cell transplant as measured by blood and urine tests. Two measurements were taken: the first immediately prior to the stem cell transplant, and the second at the time of the complete response. PART 4 OF 16 The alternative hypothesis is also known as the: In an article appearing in Today’s Health a writer states that the average number of calories in a serving of popcorn is 75. To determine if the average number of calories in a serving of popcorn is different from 75, a nutritionist selected a random sample of 20 servings of popcorn and computed the sample mean number of calories per serving to be 78 with a sample standard deviation of 7. The “Pizza Hot” manager commits a Type I error if he/she is PART 5 OF 16 From a sample of 500 items, 30 were found to be defective. The point estimate of the population proportion defective will be: Compute where t15 has a t-distribution with 15 degrees of freedom. PART 6 OF 16 The mean of a probability distribution can be: PART 7 OF 16 The following data were obtained from a survey of college students. The variable X represents the number of non-assigned books read during the past six months. PART 8 OF 16 Sue has 10 pictures but only has space in her apartment to hang 4 of them on a wall. The number of different arrangements of four pictures from a selection of ten pictures is: PART 9 OF 16 Staples, a chain of large office supply stores, sells a line of desktop and laptop computers. Company executives want to know whether the demands for these two types of computers are dependent on one another. Each day’s demand for each type of computer is categorized as Low, Medium-Low, Medium-High, or High. The data shown in the table below is based on 200 days of operation. Based on these data, can Staples conclude that demands for these two types of computers are independent? Test at the 5% level of significance. PART 10 OF 16 The marketing manager of a large supermarket chain would like to determine the effect of shelf space (in feet) on the weekly sales of international food (in hundreds of dollars). A random sample of 12 equal –sized stores is selected, with the following results: PART 11 OF 16 Are America’s top chief executive officers (CEOs) really worth all that money? One way to answer this question is to look at the annual company percentage increase in revenue versus the CEO’s annual percentage salary increase in that same company. Suppose that a random sample of companies yielded the following data: PART 12 OF 16 Suppose that the average weekly earnings for employees in general automotive repair shops is $450, and that the standard deviation for the weekly earnings for such employees is $50. A sample of 100 such employees is selected at random. Find the probability that the mean of the sample is between $445 and $455. Place your answer, rounded to 4 decimal places, in the blank. For example, 0.2345 would be a legitimate entry. 0.6026 PART 13 OF 16 A sample of 9 production managers with over 15 years of experience has an average salary of $71,000 and a sample standard deviation of $18,000. Assuming that s = 18,000 is a reasonable estimate for what sample size would be needed to ensure that we could estimate the true mean salary of all production managers with more than 15 years experience within $4200 if we wish to be 95% confident? Place your answer, as a whole number, in the blank. Do not use a dollar sign, a comma, or any other stray mark. For example, 34 would be a legitimate entry. 71 PART 14 OF 16 Find the mean of the following probability distribution? Part 15 of 16 A statistician wishes to test the claim that the standard deviation of the weights of firemen is greater than 25 pounds. To do so, she selected a random sample of 30 firemen and found s = 27.2 pounds. Assuming that the weights of firemen are normally distributed if the statistician wanted to test her research hypothesis at the .05 level of significance, what is the critical value? Part 16 of 16 Suppose that a marketing firm sends questionnaires to two different companies. Based on historical evidence, the marketing research firm believes that each company, independently of the other, will return the questionnaire with a probability of 0.30. What is the probability that neither of the questionnaires will be returned? Place your answer, rounded to 2 decimal places, in the blank. For example, 0.23 is a legitimate entry. 0.09