MATH302 Quiz 5 QUESTIONS AND ANSWER PRACTICE DOCS

MATH302 Quiz 5 QUESTIONS AND ANSWER PRACTICE DOCS Part 1 of 8 - 2.0/ 3.0 Points Question 1 of 17 1.0/ 1.0 Points Two independent samples of sizes n1 = 50 and n2 = 50 are randomly selected from two populations to test the difference between the population means,   . The sampling distribution of the sample mean difference,   is: A.approximately normal B.chi-squared distributed with 99 degrees of freedom C.t - distributed with 98 degrees of freedom D.normally distributed Question 2 of 17 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 Question 3 of 17 0.0/ 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 0.394 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 of 2.54 Part 2 of 8 - 4.0/ 5.0 Points Question 4 of 17 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. A. 177.12 + 0.8500(size) B.    177.12 + 1.065(size) C. 1.065 + 177.12(size) D. 197.12 + 2.065(size) Question 5 of 17 1.0/ 1.0 Points The correlation value ranges from A.–2 to +2 B.–1 to +1 C.0 to +1 D.-3 to +3 Question 6 of 17 0.0/ 1.0 Points 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 A.  A 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 t-test value, 7.74, is greater than the critical value 1.96. B.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. C.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. D.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. Question 7 of 17 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.highly correlated D.inversely related Question 8 of 17 1.0/ 1.0 Points In a simple linear regression analysis, the following sum of squares are produced: = 400 = 80 = 320 The proportion of the variation in Y that is explained by the variation in X is: A.25% B.50% C.20% D.80% Part 3 of 8 - 1.0/ 2.0 Points Question 9 of 17 1.0/ 2.0 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 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 0.10 level of 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 30 35 Mean trunk diameter (cm) 45 39 Sample variance 120 140 What is the test value for this hypothesis test? What is the critical value? Feedback: This is a t-test of independent samples.  Use the formula for the t test value on page 480: Using Table F (df = 29, alpha = 0.10, one-tail test) the critical t-value is 1.311. Part 4 of 8 - 2.0/ 2.0 Points Question 10 of 17 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.  Question 11 of 17 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 marketing manager of a large supermarket chain would like to determine the effect of shelf space (in feet) on the weekly sales of international food (in hundreds of dollars). A random sample of 12 equal –sized stores is selected, with the following results: Store Shelf Space(X) Weekly Sales(Y) 1 10 2.0 2 10 2.6 3 10 1.8 4 15 2.3 5 15 2.8 6 15 3.0 7 20 2.7 8 20 3.1 9 20 3.2 10 25 3.0 11 25 3.3 12 25 3.5 Based on these data, what are the least squares regression coefficients of the Y-intercept (a) and slope (b)? Place your answers, rounded to 3 decimal places , in the blanks provided. Answer Key: 1.480, 0.074 Part 5 of 8 - 1.0/ 2.0 Points Question 12 of 17 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 12 3 12 28 6 8 2 percent change for CEO 6 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 test 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.  0.373 Question 13 of 17 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. 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. 1.65 Answer Key: 1.64|1.65 Part 6 of 8 - 2.0/ 3.0 Points Question 14 of 17 2.0/ 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. Researchers conducted an experiment to measure the effect of a drug on improving the quality of sleep as determined by how many more minutes of REM sleep were measured for each participant. One group of participants were given the experimental drug; the other (control) group was given a placebo. Does the evidence indicate that the drug improved the amount of REM sleep at a 0.01 level of significance? Answer each of the following parts.   Experimental group Control group sample size 35 50 mean sleep improvement 12.8 9.1 sample variance 56.3 61.2 What is the test value for this hypothesis test? What is the P-value for this hypothesis test? What is the conclusion of this hypothesis test?  Choose one. 1.  There is sufficient evidence to show that the experimental drug improved the quality of sleep. 2.  There is not sufficient evidence to show that the experimental drug improved the quality of sleep. 3.  There is sufficient evidence to show that the quality of sleep is different for the experimental drug than for the control drug. 4.  There is not sufficient evidence to show that the control drug decreased the quality of sleep. Feedback: This is a t-test of independent samples.  Use the formula on page 480 to compute the t test value: This is a right-tail test with test value t = 2. and df = 34 (using the smaller sample size).  The P-value is 0.0174 using TDIST(2.,34,1) or the Critical Values workbook. Because the P-value is greater than alpha (0.01), there is not sufficient evidence to show that the experimental drug improved the quality of sleep. Part 7 of 8 - 1.0/ 1.0 Points Question 15 of 17 1.0/ 1.0 Points In conducting hypothesis testing for difference between two means when samples are dependent (paired samples), the variable under consideration is   ; the sample mean difference between the pairs. True False Part 8 of 8 - 2.0/ 2.0 Points Question 16 of 17 1.0/ 1.0 Points A negative relationship between an explanatory variable X and a response variable Y means that as X increases, Y decreases, and vice versa. True False Question 17 of 17 1.0/ 1.0 Points A simple linear regression equation is given by y' = 5 + 3x. The predicted value of Y when X = 3 is 5. True False