MATH 302 Stats Quiz 5

MATH 302 Stats Quiz 5 Quiz 5 MATH 302 Part 1 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 ...

MATH 302 Stats Quiz 5 Quiz 5 MATH 302 Part 1 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. No, the test value of 1.879 does not exceed the critical value of 2.46  B. No, the test value of 1.371 does not exceed the critical value of 2.12  C. No, the p-value associated with this test is 0.0528  D. Yes, the p-value associated with this test is 0.0264 Question 2 of 17 1.0/ 1.0 Points Multiple myeloma or blood plasma cancer is characterized by increased blood vessel formulation in the bone marrow that is a prognostic factor in survival. One treatment approach used for multiple myeloma is stem cell transplantation with the patient’s own stem cells. The following data represent the bone marrow microvessel density for a sample of 7 patients who had a complete response to a stem cell transplant as measured by bloodand urine tests. Two measurements were taken: the first immediately prior to the stem cell transplant, and the second at the time of the complete response. Patient 1 2 3 4 5 6 7 Before 158 189 202 353 416 426 441 After 284 214 101 227 290 176 290 Perform an appropriate test of hypothesis to determine if there is evidence, at the .05 level of significance, to support the claim that the mean bone marrow microvessel density is higher before the stem cell transplant than after the stem cell transplant? What is the value of the sample test statistic?  A. t = 1.8424  B. z = 1.8424  C. t = 2.7234  D. p = 2.7234 Question 3 of 17 1.0/ 1.0 Points Which of the following statements is true regarding the F – distribution?  Part 2 of 8 - 5.0/ 5.0 Points Question 4 of 17 1.0/ 1.0 Points Outliers are observations that  A. lie outside the typical pattern of points  B. render the study useless  C. disrupt the entire linear trend  D. lie outside the sample Answer Key: A Question 5 of 17 1.0/ 1.0 Points The correlation value ranges from  A. -3 to +3 B 1.0/ 1.0 Points Correlation is a summary measure that indicates:  A. the magnitude of difference between two variables  B. a curved relationship among the variables  C. the strength of the linear relationship between pairs of variables  D. the rate of change in Y for a one unit change in X Answer Key: C Question 7 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. 8 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 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 positive. Answer Key: C Part 3 of 8 - 0.0/ 2.0 Points Question 9 of 17 0.0/ 2.0 Points Click to see additional instructions 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 20 30 Mean trunk diameter (cm) 45 39 Sample variance 100 150 What is the test value for this hypothesis test? Test value: 1.328 Round your answer to three decimal places. What is the critical value? Critical value: 1.300 Round your answer to three decimal places. Answer Key: 1.897, 1.328 Feedback: This is a t-test of independent samples. Use the formula for the t test value on page 480: Using Table F (df = 19, alpha = 0.10, one-tail test) the critical t-value is 1.328. Part 4 of 8 - 2.0/ 2.0 Points 12 25 3.5 Find the equation of the regression line for these data. What is the value of the standard error of the estimate? Place your answer, rounded to 3 decimal places, in the blank. Do not use a dollar sign. For example, 0.345 would be a legitimate entry. 0.308 Answer Key: 0.308 Question 11 of 17 1.0/ 1.0 Points Click to see additional instructions 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 Using the equation of the regression line for these data, predict the average weekly sales (in hundreds of dollars) of international food for stores with 13 feet of shelf space for international food.Place your answer, rounded to 3 decimal places , in the blank. Do not use a dollar sign. For example, 2.345 Click to see additional instructions 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 = .848, n2 = 21, s2 = .529. If you follow Bluman's advice and place the larger variance in the numerator when computing the test value, at the .05 level of significance, what is the critical value associated with this test of hypothesis? Place your answer, rounded to 2 decimal places, in the blank. For example, 3.45 would be a legitimate entry. 2.46 Question 13 of 17 Click to see additional instructions 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 the p-value associated with such a test of hypothesis? Place your answer, rounded to 4 decimal places, in the blank. For example, .0123 would be a legitimate entry. 0.2460 Answer Key: .2460|.2502 Part 6 of 8 - 3.0/ 3.0 Points Question 14 of 17 3.0/ 3.0 Points Click to see additional instructions A special coating is applied to several scale model engine nacelle body shapes to determine if it reduces the drag coefficient. The following data are the drag coefficient before the coating is applied and after.Model #1 #2 #3 #4 #5 #6 Before 0.782 0.656 0.541 0.250 0.323 0.888 After 0.668 0.581 0.532 0.241 0.334 0.891 Perform a hypothesis test to determine if there is evidence at the 0.05 level of significance to support the claim that the coating reduces the drag coefficient. What is the test value for this hypothesis test? Answer: 1.56 Round your answer to two decimal places. What is the P-value for this hypothesis test? Answer: 0.089 Round your answer to three decimal places. What is your conclusion for this test? Choose one. 1. There is sufficient evidence to show the coating reduces the drag coefficient. 2. There is not sufficient evidence to show that the coating reduces the drag coefficient. 3. There is sufficient evidence to show that the drag coefficient changed after the coating was applied. 4. There is sufficient evidence to show that the drag coefficient increased after the coating was applied. Answer: 2 Enter only a 1, 2, 3 or 4 for your answer. Answer Key: 1.56, 0.089, 2 Part 7 of 8 - 1.0/ 1.0 Points Question 15 of 17 1.0/ 1.0 Points When te In a simple linear regression problem, the least squares line is y' = -3.2 + 1.3X, and the coefficient of determination is 0.7225. The coefficient of correlation must be –0.85. True False Answer Key: False