MATH 302 Final Exam 1 - Question and Answers | LATEST UPDATE

MATH 302 Final Exam 1 - Question and Answers AMU Math 302 – Final Fall 2018 25/25 1. A company operates four machines during three shifts each day. From production records, the data in the table below were collect ...

MATH 302 Final Exam 1 - Question and Answers AMU Math 302 – Final Fall 2018 25/25 1. 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. Machine Shift A B C D 1 41 20 12 16 2 31 11 9 14 3 15 17 16 10 A. The number of breakdowns is dependent on the shift, because the test value 11.649 is less than the critical value of 12.592. B. The claim that the number of breakdowns is independent of the shift cannot be rejected, because the test value 11.649 is less than the critical value of 12.592 C. The number of breakdowns is dependent on the shift, because the p-value is .07. D. The number of breakdowns is independent of the shift, because the test value 12.592 is greater than the critical value of 11.649. 2. The data presented in the table below resulted from an experiment in which seeds of 5 different types were planted and the number of seeds that germinated within 5 weeks after planting was recorded for each seed type. At the .01 level of significance, is the proportion of seeds that germinate dependent on the seed type? Seed Type Observed Frequencies Germinated Failed to Germinate 1 31 7 2 57 33 3 87 60 4 52 44 5 10 19 A. Yes, because the test value 16.86 is greater than the critical value of 13.28 B. Yes, because the test value 16.86 is less than the critical value of 14.86 C. No, because the test value of 16.86 is greater than the critical value of 13.28 D. No, because the test value of 13.28 is less than the critical value of 16.86 3. An agent for a residential real estate company in a large city would like to be able to predict the monthly rental cost of apartments based on the size of the apartment. Data for a sample of 25 apartments in a particular neighborhood are provided in the worksheet Apartments in the Excel workbook Apartments.xlsx. Apartments.xlsx At the .05 level of significance determine if the correlation between rental cost and apartment size is significant. A. Yes, there is a statistically significant linear relationship between monthly rental cost and apartment size, because the sample correlation coefficient 0.85 exceeds 0.50. B. Yes, there is a statistically significant linear relationship between monthly rental cost and apartment size, because the p-value for this test is less than .0001 C. Yes, there is a statistically significant linear relationship between monthly rental cost and apartment size, because the t-test value, 7.74, is greater than the critical value 1.96. D. No, there is not a statistically significant linear relationship between monthly rental cost and apartment size, because the sample correlation coefficient is less than .95. 4. 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. . Is the correlation between weekly sales and shelf space significant at the .01 level of significance? Store 1 2 3 4 5 6 Shelf Space 5 5 5 10 10 10 Weekly Sales 1.6 2.2 1.4 1.9 2.4 2.6 Store 7 8 9 10 11 12 Shelf Space 15 15 15 20 20 20 Weekly Sales 2.3 2.7 2.8 2.6 2.9 3.1 Compute the value of the sample correlation coefficient between weekly sales and shelf space. A. 0.684 B. 0.827 C. 0.308 D. 0.652 5. The correlation value ranges from A. -1 to +1 B. 0 to +1 C. -2 to +2 D. -3 to +3 6. A pharmaceutical company is testing the effectiveness of a new drug for lowering cholesterol. As part of this trial, they wish to determine whether there is a difference between the effectiveness for women and for men. Assume α = 0.05. What is the test value? Women Men Sample size 50 80 Mean effect 7 6.95 Sample variance 3 4 A. z = 0.455 B. t = 0.151 C. z = 0.081 D. t = 3.252 7. Two teams of workers assemble automobile engines at a manufacturing plant in Michigan. A random sample of 145 assemblies from team 1 shows 15 unacceptable assemblies. A similar random sample of 125 assemblies from team 2 shows 8 unacceptable assemblies. Is there sufficient evidence to conclude, at the 10% significance level, that the two teams differ with respect to their proportions of unacceptable assemblies? A. No, since the p-value is less than 0.10 B. No, since the test value exceeds the critical value C. No, since the test value does not exceed the critical value D. Yes, since the p-value is greater than 0.10 8. The form of the alternative hypothesis can be: A. one-tailed B. one or two-tailed C. two-tailed D. neither one or two-tailed 9. Smaller p-values indicate more evidence in support of the: A. null hypothesis B. quality of the researcher C. the reduction of variance D. alternative hypothesis 10. The null and alternative hypotheses divide all possibilities into: A. two non-overlapping sets B. two sets that may or may not overlap C. two sets that overlap D. as many set as necessary to cover all possibilities 11. A sample of 25 different payroll departments found that the employees worked an average of 310.3 days a year with a standard deviation of 23.8 days. What is the 90% confidence interval for the average days worked by employees in all payroll departments? A. 301.0 < ? < 319.6 B. 298.0 < ? < 322.6 C. 302.2 < ? < 318.4 D. 314.1 < ? < 316.8 12. A researcher wishes to know, with 98% confidence, the percentage of women who wear shoes that are too small for their feet. A previous study conducted by the Academy of Orthopedic Surgeons found that 80% of women wear shoes that are too small for their feet. If the researcher wants her estimate to be within 3% of the true proportion, how large a sample is necessary? A. 966 B. 683 C. 183 D. 484 13. In a normal distribution, changing the standard deviation: A. shifts the curve left or right B. makes the curve more robust C. splits the distribution to two curves D. makes the curve more or less spread out 14. There are two types of random variables, they are A. discrete and continuous B. real and unreal C. exhaustive and mutually exclusive D. complementary and cumulative 15. If a die is rolled one time, find the probability of getting a number greater than 2. A. 2 B. -1 C. 5/6 D. 4/6 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 computers 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. Desktops Low Med-low Med-high high Low 3 14 14 4 35 Laptops Med-low 6 18 17 22 63 Med-high 13 16 11 16 56 High 8 14 15 9 46 30 62 57 51 200 What is the test value for this hypothesis test? Round your answer to two decimal places. What is the critical value for this hypothesis test? Answer: 15.31 Answer: 16.92 What is the conclusion for this hypothesis test? Choose one. 1. At the .05 level of significance, Staples can conclude that demands for these two types of computers are independent. 2. At the .05 level of significance, Staples can conclude that demands for these two types of computers are dependent. Answer 1 17. A company has observed that there is a linear relationship between indirect labor expense (ILE) , in dollars, and direct labor hours (DLH). Data for direct labor hours and indirect labor expense for 18 months are given in the file Treating ILE as the response variable, use regression to fit a straight line to all 18 data points. Based on your results, If direct labor hours (DLH) increases by one hour, the indirect labor expense (ILE), on average, increases by approximately how much? Place your answer, rounded to 2 decimal places, in the blank. Do not use any stray punctuation marks or a dollar sign. For example, 34.56 would be a legitimate entry. 15.26 18. Two teams of workers assemble automobile engines at a manufacturing plant in Michigan. A random sample of 145 assemblies from team 1 shows 15 unacceptable assemblies. A similar random sample of 125 assemblies from team 2 shows 8 unacceptable assemblies. If you are interested in determining if there is sufficient evidence to conclude, at the 10% significance level, that the two teams differ with respect to their proportions of unacceptable assemblies, what is/are the critical value you would use to conduct such a test of hypothesis? Place your answer, rounded to 2 decimal places, in the blank. If there are two critical values, place only the positive value in the blank. For example, 2.34 would be a legitimate entry. 1.64 19. A set of final exam scores in an organic chemistry course was found to be normally distributed, with a mean of 73 and a standard deviation of 8. What is the probability of getting a score between 65 and 89 on this exam? Place your answer, rounded to 4 decimal places in the blank. For example, 0.3456 would be a legitimate entry. .8185 20. You are trying to estimate the average amount a family spends on food during a year. In the past, the standard deviation of the amount a family has spent on food during a year has been ? = $1200. If you want to be 99% sure that you have estimated average family food expenditures within $60, how many families do you need to survey? Place your answer, a whole number, in the blank 2653. For example, 1234 would be a legitimate entry. 21. In February 2002 the Argentine peso lost 70% of its value compared to the United States dollar. This devaluation drastically raised the price of imported products. According to a survey conducted by AC Nielsen in April 2002, 68% of the consumers in Argentina were buying fewer products than before the devaluation, 24% were buying the same number of products, and 8% were buying more products. Furthermore, in a trend toward purchasing less-expensive brands, 88% indicated that they had changed the brands they purchased. Suppose the following complete set of results were reported. Use the following data to answer this question. Number of Products Purchased Total Brands Purchased Fewer Same More Same 10 14 24 48 Changed 262 82 8 352 Total 272 96 32 400 What is the probability that a consumer selected at random purchased the same number or more products than before? Place your answer, rounded to 4 decimal places, in the blank. .3200 22. The ABC battery company claims that their batteries last 100 hours, on average. You decide to conduct a test to see if the company's claim is true. You believe that the mean life may be different from the 100 hours the company claims. You decide to collect data on the average battery life (in hours) of a random sample of n = 20 batteries. Some of the information related to the hypothesis test is presented below. Test of H0: ? = 100 versus H1: ? ≠ 100 Sample mean 98.5 Std error of mean 0.777 Assuming the life length of batteries is normally distributed, if you wish to conduct this test at the 0.05 level of significance, what are the critical values that you should use? Place the smaller critical value, rounded to 3 decimal places, in the first blank. For example, -1.234 would be a legitimate entry. -2.093. Place the larger critical value, rounded to 3 decimal places, in the second blank. For example, 1.234 would be a legitimate entry. 2.093 23. A reading list for a course contains 20 articles. How many ways are there to choose three articles from this list? Place your answer in the blank. Do not use any decimal places or commas. For example, 45 would be a legitimate entry. 1140