Math 302 Final Exam

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 Question 2 of 23 1.0/ 1.0 Points The chi-square goodness-of-fit test can be used to test for: Part 2 of 16 - 2.0/ 3.0 Points Question 3 of 23 1.0/ 1.0 Points Data for a sample of 25 apartments in a particular neighborhood are provided in the worksheet Apartments in the Excel workbook A. Using that data, find the estimated regression equation which can be used to estimate the monthly rent for apartments in this neighborhood using size as the predictor variable. Question 4 of 23 1.0/ 1.0 Points Correlation is a summary measure that indicates: Question 5 of 23 0.0/ 1.0 Points In regression analysis, the variable we are trying to explain or predict is called the Part 3 of 16 - 1.0/ 2.0 Points Question 6 of 23 0.0/ 1.0 Points An investor wants to compare the risks associated with two different stocks. One way to measure the risk of a given stock is to measure the variation in the stock’s daily price changes. In an effort to test the claim that the variance in the daily stock price changes for stock 1 is different from the variance in the daily stock price changes for stock 2, the investor obtains a random sample of 21 daily price changes for stock 1 and 21 daily price changes for stock 2. The summary statistics associated with these samples are: n1 = 21, s1 = .725, n2 = 21, s2 = . 529. If you compute the test value by placing the larger variance in the numerator, at the .05 level of significance, would you conclude that the risks associated with these two stocks are different? Question 7 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 Part 4 of 16 - 2.0/ 3.0 Points Question 8 of 23 1.0/ 1.0 Points The null and alternative hypotheses divide all possibilities into: Question 9 of 23 0.0/ 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? State the null and alternative hypotheses. Question 10 of 23 1.0/ 1.0 Points Which of the following values is not typically used for ? Part 5 of 16 - 2.0/ 2.0 Points Question 11 of 23 1.0/ 1.0 Points Confidence intervals are a function of which of the following three things? 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 = . Part 6 of 16 - 1.0/ 1.0 Points Question 13 of 23 1.0/ 1.0 Points The standard deviation of a probability distribution is a: Part 7 of 16 - 1.0/ 1.0 Points Question 14 of 23 1.0/ 1.0 Points A multiple choice quiz consists of 6 questions, each with 4 possible answers. If a student guesses at the answer to each question, then the mean number of correct answers is Part 8 of 16 - 1.0/ 1.0 Points Question 15 of 23 1.0/ 1.0 Points If two events are mutually exclusive, what is the probability that both occur at the same time? 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. 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 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. 5.99, 2 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. 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 Part 11 of 16 - 0.0/ 1.0 Points Question 18 of 23 0.0/ 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 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 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 length of time to complete a door assembly on an automobile factory assembly line is normally distributed with mean 6.7 minutes and standard deviation 2.2 minutes. For a door selected at random, what is the probability the assembly line time will be between 5 and 10 minutes? Place your answer, rounded to 4 decimal places, in the blank. For example, 0.1776 would be a legitimate answer. 0.7133 Answer Key: 0.6500| 0.7500 Part 13 of 16 - 0.0/ 1.0 Points Question 20 of 23 0.0/ 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. 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 . For example, 1234 would be a legitimate entry. Answer Key: 2620| 2685 Part 14 of 16 - 1.0/ 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. Find the mean of the following probability distribution. X 1 2 3 4 5 P(X) 0.20 0.10 0.35 0.05 0.30 Round your answer to two decimal place as necessary. For example, 4.56 would be a legitimate entry. Mean = 3.15 Answer Key: 3.15 Part 15 of 16 - 0.0/ 1.0 Points Question 22 of 23 0.0/ 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 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, what is the p-value associated with this test? Place your answer, rounded to 3 decimal places, in the blank. For example, 0.234 would be a legitimate entry. 1.711 Answer Key: 0.062 Part 16 of 16 - 0.0/ 1.0 Points Question 23 of 23 0.0/ 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. An ice cream vendor sells three flavors: chocolate, strawberry, and vanilla. Forty five percent of the sales are chocolate, while 30% are strawberry, with the rest vanilla flavored. Sales are by the cone or the cup. The percentages of cones sales for chocolate, strawberry, and vanilla, are 75%, 60%, and 40%, respectively. For a randomly selected sale, define the following events: = chocolate chosen = strawberry chosen = vanilla chosen = ice cream on a cone icecream in a cup Find the probability that the ice cream was vanilla flavor, given that it was sold on a cone. Place your answer, rounded to 4 decimal places, in the blank. For exampe, 0.3456 would be a legitimate entry. .3922 Answer Key: 0.1619