MATH 302 Final Exam 2 - Question and Answers

MATH 302 Final Exam 2 - Question and Answers Part 1 of 16 - 2.0/ 2.0 Points Question 1 of 23 1.0/ 1.0 Points 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 16.86 is greater than the critical value of 13.28 D.No, because the test value 13.28 is less than the critical value of 16.86 Answer Key: A 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 meansMATH 302 Final Exam 2 - Question and Answers B.difference between population variances C.normality D.significance of sample statistics Answer Key: C Part 2 of 16 - 3.0/ 3.0 Points Question 3 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 decreases, and the correlation coefficient must be positive. B.As x increases, y increases, and the correlation coefficient must be positive. C.As x increases, y decreases, and the correlation coefficient must be negative. D.As x increases, y increases, and the correlation coefficient must be negative. Answer Key: C Question 4 of 23 1.0/ 1.0 Points In a simple linear regression analysis, the following sum of squares are produced: MATH 302 Final Exam 2 - Question and Answers = 400 = 80 = 320 The proportion of the variation in Y that is explained by the variation in X is: A.20% B.50% C.80% D.25% Answer Key: C Question 5 of 23 1.0/ 1.0 Points The city of Oakdale wishes to see if there is a linear relationship between the temperature and the amount of electricity used (in kilowatts). Based on the data in the table below, is there a significant linear relationship between temperature and the amount of electricity used? These data are also available in the worksheet temperature in the Excel workbook T. T Temperature (x) 73 78 85 98 93 81 76 105 Kilowatts (y) A.Yes, the sample correlation coefficient is equal to 0.878, which provides evidence of a significant linear relationship. MATH 302 Final Exam 2 - Question and Answers B.No, the sample correlation coefficient is equal to 0.098, which does not provide evidence of a significant linear relationship. C.No, the sample correlation coefficient is equal to 0.981, which does not provide evidence of a significant linear relationship. D.Yes, the sample correlation coefficient is equal to 0.981, which provides evidence of a significant linear relationship. Answer Key: D Part 3 of 16 - 2.0/ 2.0 Points Question 6 of 23 1.0/ 1.0 Points Which of the following statements is true regarding the F – distribution? A.It is a distribution of negative values B.It is always skewed to the left C.It typically appears in tests of equal proportions D.none of the above Answer Key: D Question 7 of 23 1.0/ 1.0 Points A field researcher is gathering data on the trunk diameters of mature pine and spruce trees in a certain area. The following are the results of his random sampling. Can he conclude, at the .10 level of MATH 302 Final Exam 2 - Question and Answers significance, that the average trunk diameter of a pine tree is greater than the average diameter of a spruce tree? Pine trees Spruce trees Sample size 40 70 Mean trunk diameter (cm) 45 39 Sample variance 100 150 A.The data support the claim because the test value 2.78 is greater than 1.28. B.The data do not support the claim because the test value 1.29 is less than 1.64. C. The data do not support the claim because the test value 1.29 is greater than 1.28. D. The data support the claim because the test value 2.78 is greater than 1.64. Answer Key: A Part 4 of 16 - 3.0/ 3.0 Points Question 8 of 23 1.0/ 1.0 Points The hypothesis that an analyst is trying to prove is called the: A.quality of the researcher B.level of significance C.alternative hypothesis D.elective hypothesisMATH 302 Final Exam 2 - Question and Answers Answer Key: C Question 9 of 23 1.0/ 1.0 Points Results from previous studies showed 79% of all high school seniors from a certain city plan to attend college after graduation. A random sample of 200 high school seniors from this city reveals that 162 plan to attend college. Does this indicate that the percentage has increased from that of previous studies? Test at the 5% level of significance. What is your conclusion? A.Do not reject H0. There is not enough evidence to support the claim that the proportion of students planning to go to college is greater than .79. B.Cannot determine C.Reject H0. There is enough evidence to support the claim that the proportion of students planning to go to college is now greater than .79. D.More seniors are going to college Answer Key: A Question 10 of 23 1.0/ 1.0 Points A lab technician is tested for her consistency by taking multiple measurements of cholesterol levels from the same blood sample. The target accuracy is a variance in measurements of 1.2 or less. If the lab technician takes 16 measurements and the variance of the measurements in the sample is 2.2, does this provide enough evidence to reject the claim that the lab technician’s accuracy is within the target accuracy? At the  = .01 level of significance, what is your conclusion? A.MATH 302 Final Exam 2 - Question and Answers Reject H0. At the = .01 level of significance, there is not enough evidence to support the claim that this technician’s true variance is larger than the target accuracy. B.Cannot determine C.Reject H0. At the = .01 level of significance, there is enough evidence to support the claim that this technician’s variance is larger than the target accuracy. D.Do not reject H0. At the = .01 level of significance there is not sufficient evidence to suggest that this technician’s true variance is greater than the target accuracy. Answer Key: D Part 5 of 16 - 2.0/ 2.0 Points Question 11 of 23 1.0/ 1.0 Points Compute where t15 has a t-distribution with 15 degrees of freedom. A.0.03197 B.0.96803 C.0.93606 D.0.7639 Answer Key: AMATH 302 Final Exam 2 - Question and Answers Question 12 of 23 1.0/ 1.0 Points When you calculate the sample size for a proportion, you use an estimate for the population proportion; namely . A conservative value for n can be obtained by using = ______ . A.0.05 B.0.10 C.0.50 D.0.01 Answer Key: C Part 6 of 16 - 1.0/ 1.0 Points Question 13 of 23 1.0/ 1.0 Points The mean of a probability distribution can be: A.a positive number B.a negative number C.zero D.all of the above Answer Key: DMATH 302 Final Exam 2 - Question and Answers 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 greater than 40 batteries will last at least 8 hours? A.0.0402 B.0.0789 C.0.4538 D.0.9598 Answer Key: A Part 8 of 16 - 1.0/ 1.0 Points Question 15 of 23 1.0/ 1.0 Points In a recent study, the following data were obtained in response to the question, “Do you favor recycling in your neighborhood?” Yes No No Opinion Males 25 15 10 Females 30 10 10MATH 302 Final Exam 2 - Question and Answers If a person is picked at random, what is the probability that the person is either male or has no opinion regarding recycling? A.3/5 B.3/10 C.4/5 D.7/10 Answer Key: A Part 9 of 16 - 3.0/ 3.0 Points Question 16 of 23 3.0/ 3.0 Points Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. 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, MediumHigh, 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 MATH 302 Final Exam 2 - Question and Answers laptops med-low med-high high What is the test value for this hypothesis test? Answer: 15.31 Round your answer to two decimal places. What is the critical value for this hypothesis test? Answer: 16.92 Round your answer to two decimal places. 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 Enter only a 1 or 2 for your answer. Answer Key: 15.31, 16.92, 1 Part 10 of 16 - 1.0/ 1.0 Points Question 17 of 23 1.0/ 1.0 Points Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. MATH 302 Final Exam 2 - Question and Answers Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. 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. Using your estimated regression output, predict the indirect labor expenses for a month in which the company has 31 direct labor hours. Place your answer, rounded to 1 decimal place, in the blank. Do not use any stray punctuation marks or a dollar sign. For example, 458.9 would be a legitimate entry. 525.4 Answer Key: 525.4 Part 11 of 16 - 0.0/ 1.0 Points Question 18 of 23 1.0/ 1.0 Points Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. 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 6 8 2 percent change for CEO -1 7 2MATH 302 Final Exam 2 - Question and Answers 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 p-value associated with this test of hypothesis? Place your answer, rounded to 3 decimal places, in the blank. For example, 0.134 would be a legitimate entry. 0.173 Answer Key: 0.173 Part 12 of 16 - 0.0/ 1.0 Points Question 19 of 23 1.0/ 1.0 Points Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. A Wendy’s fast-food restaurant sells hamburgers and chicken sandwiches. On a typical weekday, the demand for hamburgers is normally distributed with a mean of 450 and standard deviation of 80 and the demand for chicken sandwiches is normally distributed with a mean of 120 and standard deviation of 30. How many hamburgers must the restaurant stock to be 99% sure of not running out on a given day? Place you answer, rounded to the nearest whole number in the blank. For example, 345 would be a legitimate entry. 631 Answer Key: 631|641 Part 13 of 16 - 1.0/ 1.0 Points Question 20 of 23 1.0/ 1.0 Points Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. MATH 302 Final Exam 2 - Question and Answers Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. If a sample has 25 observations and a 99% confidence estimate for is needed, the appropriate value of the t-multiple required is 2.797 . Place your answer, rounded to 3 decimal places, in the blank. For example, 3.456 would be an appropriate entry. Answer Key: 2.797 Part 14 of 16 - 0.0/ 1.0 Points Question 21 of 23 1.0/ 1.0 Points Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. The annual returns, in percentages, on stocks A and B for three possible states of the economy are given in the table below. Economy State Probability StockA StockB Good 0.5 40 20 Average 0.3 20 40 Bad 0.2 10 8 If one invested in StockA, what would be the standard deviation of the percentage return? Place your answer, in percent rounded to 1 decimal place, in the blank. For example, a standard deviation of 10.39 percent would be reported as 10.4. Do not use a percent sign. 12MATH 302 Final Exam 2 - Question and Answers Answer Key: 12.0|13.0 Part 15 of 16 - 0.0/ 1.0 Points Question 22 of 23 1.0/ 1.0 Points Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. The CEO of a software company is committed to expanding the proportion of highly qualified women in the organization’s staff of salespersons. He believes that the proportion of women in similar sales positions across the country is less than 45%. Hoping to find support for his belief, he directs you to test H0: p .45 vs H1: p < .45. In doing so, you collect a random sample of 50 salespersons employed by his company, which is thought to be representative of sales staffs of competing organizations in the industry. The collected random sample of size 50 showed that only 18 were women. Compute the p-value associated with this test. Place your answer, rounded to 4 decimal places, in the blank. For example, 0.3456 would be a legitimate entry. 0.1003 Answer Key: .1003|.1020 Part 16 of 16 - 0.0/ 1.0 Points Question 23 of 23 1.0/ 1.0 Points Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. MATH 302 Final Exam 2 - Question and Answers Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. 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 Yes No Given that multiple vehicles were involved, what proportion of accidents involved alcohol? Place your answer, rounded to 2 decimal places, in the blank. For example, 0.23 is a legitimate entry. 0.35 Answer Key: 0.3