MATH302 PRACTICE EXAM QUESTIONS AND ANSWERS FROM THE FINAL EXAM

MATH302 PRACTICE EXAM QUESTIONS AND ANSWERS FROM THE FINAL EXAM 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 Question 2 of 23 1.0/ 1.0 Points The chi-square goodness-of-fit test can be used to test for: A.significance of sample statistics B.normality C.difference between population variances D.difference between population means Part 2 of 16 - 3.0/ 3.0 Points Question 3 of 23 1.0/ 1.0 Points In choosing the “best-fitting” line through a set of points in linear regression, we choose the one with the: A.largest number of points on the line B.smallest sum of squared residuals C.smallest number of outliers D.largest sum of squared residuals Question 4 of 23 1.0/ 1.0 Points A single variable X can explain a large percentage of the variation in some other variable Y when the two variables are: A.directly related B.mutually exclusive C.inversely related D.highly correlated Question 5 of 23 1.0/ 1.0 Points Outliers are observations that A.disrupt the entire linear trend B.lie outside the typical pattern of points C.lie outside the sample D.render the study useless Part 3 of 16 - 2.0/ 2.0 Points Question 6 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.Yes, because the test value 2.56 is greater than the critical value of 2.54 B.Yes, because the test value 0.390 is less than the critical value 2.54 C.No, because the test value 1.60 is less than the critical value of 2.54 D.Yes, because the test value 2.56 is greater than the critical value 0.394 Question 7 of 23 1.0/ 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? A.Yes, the p-value associated with this test is 0.0264 B.No, the p-value associated with this test is 0.0528 C.No, the test value of 1.879 does not exceed the critical value of 2.46 D.No, the test value of 1.371 does not exceed the critical value of 2.12 Part 4 of 16 - 3.0/ 3.0 Points Question 8 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. State the null and alternative hypotheses. A. H0: = .79, H1: > .79 B.H0:  = .79, H1:  > .79 C.H0: p = .79, H1: p ≠ .79 D.H0: p ≤ .79, H1: p > .79 Question 9 of 23 1.0/ 1.0 Points The null and alternative hypotheses divide all possibilities into: A.as many sets as necessary to cover all possibilities B.two sets that may or may not overlap C.two sets that overlap D.two non-overlapping sets Question 10 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 Part 5 of 16 - 1.0/ 2.0 Points Question 11 of 23 0.0/ 1.0 Points Which of the following will make a confidence interval narrower and more precise? A.Larger sample size and lower confidence level B.Larger sample size and higher confidence level C.Smaller sample size and higher confidence level D.Smaller sample size and lower confidence level Question 12 of 23 1.0/ 1.0 Points Compute where t15 has a t-distribution with 15 degrees of freedom. A.0.03197 B.0.93606 C.0.96803 D.0.7639 Part 6 of 16 - 1.0/ 1.0 Points Question 13 of 23 1.0/ 1.0 Points One reason for standardizing random variables is to measure variables with: A.dissimilar means and similar standard deviations in like terms B.different means and standard deviations on a non-standard scale C.similar means and standard deviations on two scales D.different means and standard deviations on a single scale Part 7 of 16 - 1.0/ 1.0 Points Question 14 of 23 1.0/ 1.0 Points In a small town, 60% of the households have dogs. If 5 households are randomly selected, what is the probability that at least 4 of them have dogs? A.3 B.0.8 C.0.259 D.0.337 Part 8 of 16 - 1.0/ 1.0 Points Question 15 of 23 1.0/ 1.0 Points A gumball machine contains 300 grape flavored balls, 400 cherry flavored balls, and 500 lemon flavored balls. What is the probability of getting 1 grape ball, 1 cherry ball, and 1 lemon ball if each ball was removed and then replaced before choosing the next from the machine? A.0.0264 B.0.0531 C.0.0347 D.0.0482 Part 9 of 16 - 1.0/ 3.0 Points Question 16 of 23 1.0/ 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 Basketball Football Soccer Men 20 25 30 75 Women 18 12 15 45 38 37 45 120 What is the test value for this hypothesis test? What is the critical value for this hypothesis test? 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. 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. 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 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. 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. Part 12 of 16 - 0.0/ 1.0 Points Question 19 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. 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 25.9 mpg and a standard deviation of 9.5 mpg. If 30 such cars are tested, what is the probability the average mpg achieved by these 30 cars will be greater than 28? Place your answer, rounded to 4 decimal places, in the blank. 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. 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 25.9 mpg and a standard deviation of 9.5 mpg. If 30 such cars are tested, what is the probability the average mpg achieved by these 30 cars will be greater than 28? Feedback: This is a sampling distribution problem with μ = 25.9. σ = 9.5, and sample size n = 30. P(z > 1.) = 1 – NORMSDIST(1.) = 0.1130 Or you can compute the probability without having to compute z first: P(x-bar > 28) = 1 – NORMDIST(28, 25.9, 9.5/SQRT(30), TRUE) = 0.1130 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. Suppose that the probability that a new medication will cause a bad side effect is 0.03. If this medication is given to 150 people, what is the probability that more than three of them will experience a bad side effect? Place your answer, rounded to 4 decimal places, in the blank. For example, 0.1776 would be a legitimate answer. Part 15 of 16 - 1.0/ 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. At a university, the average cost of books per student has been $400 per student per semester. The Dean of Students believes that the costs are increasing and that the average is now greater than $400. He surveys a sample of 40 students and finds that for the most recent semester their average cost was $430 with a standard deviation of $80. What is the test value for this hypothesis test? Part 16 of 16 - 1.0/ 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. 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 ice cream in a cup Find the probability that the ice cream was strawberry flavor, given that it was sold in a cup. Place your answer, rounded to 4 decimal places, in the blank. For exampe, 0.3456 would be a legitimate entry.