MATH 302 FINAL EXAM 1 – QUESTION AND ANSWERS ( latest update )

MATH 302 FINAL EXAM 1 – QUESTION AND ANSWERS Part 1 of 16 - 2.0/ 2.0 Points Question 1 of 23 1.0 / 1.0 Points 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. Answer Key: B Question 2 of 23 1.0 / 1.0 Points The chi-square goodness-of-fit test can be used to test for: • A. difference between population means • B. significance of sample statistics • C. normality • D. difference between population variances Answer Key: C Part 2 of 16 - 3.0/ 3.0 Points Question 3 of 23 1.0 / 1.0 Points In regression analysis, the variable we are trying to explain or predict is called the • A. independent variable • B. regression variable • C. residual variable • D. dependent variable Answer Key: D Question 4 of 23 1.0 / 1.0 Points In a simple linear regression analysis, the following sum of squares are produced: = 500 = 100 = 400 The proportion of the variation in Y that is explained by the variation in X is: • A. 20% • B. 50% • C. 25% • D. 80% Answer Key: D Question 5 of 23 1.0 / 1.0 Points A linear regression analysis produces the equation y = 5.32 + (-0.846)x Which of the following statements must be true? • A. As x increases, y increases, and the correlation coefficient must be negative. • B. As x increases, y decreases, and the correlation coefficient must be negative. • C. As x increases, y decreases, and the correlation coefficient must be positive. • D. As x increases, y increases, and the correlation coefficient must be positive. Answer Key: B Part 3 of 16 - 2.0/ 2.0 Points Question 6 of 23 1.0 / 1.0 Points Some defendants in criminal proceedings plead guilty and are sentenced without a trial, whereas others who plead innocent are subsequently found guilty and then are sentenced. In recent years, legal scholars have speculated as to whether sentences of those who plead guilty differ in severity from sentences for those who plead innocent and are subsequently judged guilty. Consider the data given below on defendants accused of robbery, all of whom, by the way, had previous prison records. At the .01 level of significance, do these data suggest that the proportion of all defendants in these circumstances who plead guilty and are sent to prison differs from the proportion who are sent to prison after pleading innocent and being found guilty? Plea Guilty Not Guilty Number judged guilty n1 = 191 n2 = 64 Number sentenced to prison x1 = 101 x2 = 56 Sample proportion .529 .875 • A. No, because the test value -4.94 is outside the interval (-1.96, 1.96) • B. Yes, because the test value 2.58 is inside the interval (-4.94, 4.94) • C. No, because the test value -1.96 is inside the interval (-2.58, 2.58) • D. Yes, because the test value -4.94 is outside the interval (-2.58, 2.58) Answer Key: D Question 7 of 23 1.0 / 1.0 Points Serum ferritin is used in diagnosing iron deficiency. In a study conducted recently researchers discovered that in a sample of 28 elderly men the sample standard deviation of serum ferritin was 52.6 mg/L. For 26 younger men the sample standard deviation was 84.2 mg/L. At the .01 level of significance, do these data support the conclusion that the ferritin distribution in elderly men has a smaller variance than in younger men? • A. No, because the test value 1.60 is less than the critical value of 2.54 • B. Yes, because the test value 0.390 is less than the critical value 2.54 • C. Yes, because the test value 2.56 is greater than the critical value 0.394 • D. Yes, because the test value 2.56 is greater than the critical value of 2.54 Answer Key: D Part 4 of 16 - 3.0/ 3.0 Points Question 8 of 23 1.0 / 1.0 Points Suppose that the mean time for a certain car to go from 0 to 60 miles per hour was 7.7 seconds. Suppose that you want to test the claim that the average time to accelerate from 0 to 60 miles per hour is longer than 7.7 seconds. What would you use for the alternative hypothesis? • A. H1: = 7.7 seconds • B. H1: 7.7 seconds • C. H1: 7.7 seconds • D. H1: 7.7 seconds Answer Key: D Question 9 of 23 1.0 / 1.0 Points Which of the following values is not typically used for ? • A. 0.05 • B. 0.10 • C. 0.50 • D. 0.01 Answer Key: C Question 10 of 23 1.0 / 1.0 Points 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. State the null and alternative hypotheses. • A. H0: = 75, H1: 75 • B. H0: 75, H1: 75 • C. H0: = 75, H1: ≠ 75 • D. H0: 75, H1: 75 Answer Key: C Part 5 of 16 - 2.0/ 2.0 Points Question 11 of 23 1.0 / 1.0 Points The upper limit of the 90% confidence interval for the population proportion p, given that n = 100; and = 0.20 is • A. 0.2658 • B. 0.7342 • C. 0.5316 • D. 0.4684 Answer Key: A Question 12 of 23 1.0 / 1.0 Points The average gas mileage of a certain model car is 26 miles per gallon. If the gas mileages are normally distributed with a standard deviation of 1.3, find the probability that a randomly selected car of this model has a gas mileage between 25.8 and 26.3 miles per gallon. • A. 0.15 • B. 0.85 • C. 0.70 • D. 0.30 Answer Key: A Part 6 of 16 - 1.0/ 1.0 Points Question 13 of 23 1.0 / 1.0 Points Given that the random variable X is normally distributed with a mean of 80 and a standard deviation of 10, P(85 X 90) is • A. 0.5328 • B. 0.3413 • C. 0.1498 • D. 0.1915 Answer Key: C Part 7 of 16 - 1.0/ 1.0 Points Question 14 of 23 1.0 / 1.0 Points Suppose that 50 identical batteries are being tested. After 8 hours of continuous use, assume that a given battery is still operating with a probability of 0.70 and has failed with a probability of 0.30. What is the probability that fewer than 40 batteries will last at least 8 hours? • A. 0.9598 • B. 0.0789 • C. 0.9211 • D. 0.7986 Answer Key: C Part 8 of 16 - 1.0/ 1.0 Points Question 15 of 23 1.0 / 1.0 Points The staff at a small company includes: 4 secretaries, 20 technicians, 4 engineers, 2 executives, and 50 factory workers. If a person is selected at random, what is the probability that he or she is a factory worker? • A. 1/4 • B. 1/8 • C. 5/8 • D. 2/5 Answer Key: C Part 9 of 16 - 2.0/ 3.0 Points Question 16 of 23 2.0/ 3.0 Points A sport preference poll yielded the following data for men and women. Use a 5% significance level and test to determine if sport preference and gender are independent. Sport Preferences of Men and Women Basket ball Footb all Socc er Men 20 25 30 75 Wom en 18 12 15 45 38 37 45 12 0 What is the test value for this hypothesis test? Answer: 2.32 Round your answer to two decimal places. What is the critical value for this hypothesis test? Answer: 5.99 Round your answer to two decimal places. What is the conclusion for this hypothesis test? Choose one. 1. There is sufficient evidence to support the claim that one's sport preference is dependent on one's gender. 2. There is not sufficient evidence to support the claim that one's sport preference is dependent on one's gender. Answer: 1 Enter only a 1 or 2 for your answer. Answer Key: 2.32, 5.99, 2 Part 10 of 16 - 1.0/ 1.0 Points Question 17 of 23 1.0/ 1.0 Points 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 ILE_and_DLH.xlsx Treating ILE as the response variable, use regression to fit a straight line to all 18 data points. Approximately what percentage of the variation in indirect labor expenses is explained by the regression model you derived? Place your answer, rounded to 1 decimal place, in the blank. Do not use any stray punctuation marks or a percentage sign. For example, 78.9 would be a legitimate entry. 95.6 Answer Key: 95.6 Part 11 of 16 - 0.0/ 1.0 Points Question 18 of 23 0.0/ 1.0 Points 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: percent change for corporation 15 6 12 3 12 28 6 8 2 percent change for CEO 17 -4 12 32 -1 7 2 Do these data indicate that the population mean percentage increase in corporate revenue is greater than the population mean percentage increase in CEO salary? Use a 5% level of significance. What is the critical value that you would use to conduct this test of hypothesis? Place your answer, rounded to 3 decimal places, in the blank. For example, 2.345 would be a legitimate entry. 1.773 Answer Key: 1.895 Part 12 of 16 - 1.0/ 1.0 Points Question 19 of 23 1.0/ 1.0 Points 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. 0.8186 Answer Key: 0.7686|0.8686 Part 13 of 16 - 1.0/ 1.0 Points Question 20 of 23 1.0/ 1.0 Points The manufacturer of a new compact car claims the miles per gallon (mpg) for the gasoline consumption is mound-shaped and symmetric with a mean of 24.6 mpg and a standard deviation of 11.2 mpg. If 30 such cars are tested, what is the probability the average mpg achieved by these 30 cars will be greater than 27? Answer: 0.1207 Round your answer to 4 decimal places as necessary. For example, 0.1357 would be a legitimate entry. Answer Key: 0.1203|0.1210 Part 14 of 16 - 1.0/ 1.0 Points Question 21 of 23 1.0/ 1.0 Points Ann is applying for a bank loan to open a pizza franchise. She must first complete a written application and then, if the written application is approved, be interviewed by bank officers. If an applicant’s written application is not approved the applicant is not granted an interview with the bank officers. Past records for this bank show that the probability of an applicant having his or her written application approved is 0.63. Records also indicate that the interviewing committee of bank officers approves 85% of the individuals they interview. Find the probability that Ann’s loan request is approved. Place your answer, rounded to 2 decimal places, in the blank. For example, 0.76 would be a legitimate entry. 0.55 Answer Key: 0.45|0.65 Part 15 of 16 - 1.0/ 1.0 Points Question 22 of 23 1.0/ 1.0 Points A firm that produces light bulbs claims that their lightbulbs last 1500 hours, on average. You wonder if the average might differ from the 1500 hours that the firm claims. To explore this possibility you take a random sample of n = 25 light bulbs purchased from this firm and record the lifetime (in hours) of each bulb. You then conduct an appopriate test of hypothesis. Some of the information related to the hypothesis test is presented below. Test of H0: = 1500 versus H1: 1500 Sample mean 1509.5 Sample standard deviation 24.27 Assuming the life length of this type of lightbulb is normally distributed, if you wish to conduct this test using a .05 level of significance, what are the critical values that you should use? Place the smallest critical value, rounded to 3 decimal places, in the first blank. For example, -1.234 would be a legitimate entry. -2.064 . Place the larger critical value, rounded to 3 decimal places, in the second blank. For example, 1.234 would be a legitimate entry. 2.064 Answer Key: -2.064, 2.064 Part 16 of 16 - 0.0/ 1.0 Points Question 23 of 23 0.0/ 1.0 Points Mothers Against Drunk Driving (MADD) is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasized the problem we all face with drinking and driving. Five hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below: Number of Vehicles Involved Did alcohol play a role? 1 2 3 200 300 Yes 60 110 30 No 40 215 45 100 325 75 Given that alcohol was not involved, what proportion of the accidents involved a single vehicle? Place your answer, rounded to 2 decimal places, in the blank. For example, 0.23 is a legitimate answer. 0.33 Answer Key: 0.13