STATS Quiz 5 MCQs Question 1 of 17 1.0 PointsA 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 significance, that the average trunk diameter of a pine tree is greater than the average diameter of a spruce tree?Pine trees Spruce treesSample size 40 70Mean trunk diameter (cm) 45 39Sample variance 100 150A. The data do not support the claim because the test value 1.29 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 support the claim because the test value 2.78 is greater than 1.28.D. The data support the claim because the test value 2.78 is greater than 1.64.Question 2 of 17 1.0 PointsA researcher hypothesizes that the variation in the amount of money spent on business dinners is greater than the variation of the amount of money spent on lunches. The variance of nine business dinners was $6.12 and the variance of 12 business lunches was $0.87. What is the test value?A.7.03B.49.50C.9.61D.3.10Question 3 of 17 1.0 PointsSome 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?PleaGuilty Not GuiltyNumber judged guilty n1 = 191 n2 = 64Number sentenced to prison x1 = 101 x2 = 56Sample proportion .529 .875A.No, because the test value -1.96 is inside the interval (-2.58, 2.58)B.No, because the test value -4.94 is outside the interval (-1.96, 1.96)C.Yes, because the test value 2.58 is inside the interval (-4.94, 4.94)D.Yes, because the test value -4.94 is outside the interval (-2.58, 2.58)Part 2 of 8 -Question 4 of 17 1.0 PointsThe standard error of the estimate, sest, is essentially theA.mean of the residualsB.standard deviation of the residualsC.standard deviation of the explanatory variable D.mean of the explanatory variableQuestion 5 of 17 1.0 PointsIn a simple linear regression analysis, the following sum of squares are produced:The proportion of the variation in Y that is explained by the variation in X is:A.80%B.25%C.50%D.20%Question 6 of 17 1.0 PointsThe marketing manager of a large supermarket chain would like to use shelf space to predict the sales of pet food. For a random sample of 12 similar stores, she gathered the following information regarding the shelf space, in feet, devoted to pet food and the weekly sales in hundreds of dollars. Store 1 2 3 4 5 6Shelf Space 5 5 5 10 10 10Weekly Sales 1.6 2.2 1.4 1.9 2.4 2.6Store 7 8 9 10 11 12Shelf Space 15 15 15 20 20 20Weekly Sales 2.3 2.7 2.8 2.6 2.9 3.1What is the estimated regression equation?A. = 2.63 – 0.174xB. = 1.45 + 0.074xC. = 1.45 + 0.724xD. = 2.63 + 0.724xQuestion 7 of 17 1.0 PointsA single variable X can explain a large percentage of the variation in some other variable Y when the two variables are:A.mutually exclusiveB.inversely relatedC.highly correlatedD.directly relatedQuestion 8 of 17 1.0 PointsThe marketing manager of a large supermarket chain would like to use shelf space to predict the sales of pet food. For a random sample of 12 similar stores, she gathered the following information regarding the shelf space, in feet, devoted to pet food and the weekly sales in hundreds of dollars. .Store 1 2 3 4 5 6Shelf Space 5 5 5 10 10 10Weekly Sales 1.6 2.2 1.4 1.9 2.4 2.6Store 7 8 9 10 11 12Shelf Space 15 15 15 20 20 20Weekly Sales 2.3 2.7 2.8 2.6 2.9 3.1Is the correlation between weekly sales and shelf space significant at the .01 level of significance?A.No, the sample correlation coefficient does not exceed the critical value.B. Yes, the computed t-test statistic is less than the critical value. C.Yes, the p-value of the test for significance is less than .01.D.Yes, the value of the test statistic does not exceed the critical value.Part 3 of 8 -Question 9 of 17 2.0 PointsAccepted 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 treesSample size 25 35Mean trunk diameter (cm) 55 48Sample variance 100 140What is the test value for this hypothesis test?Test value: Round your answer to three decimal places.What is the critical value?Critical value: Round your answer to three decimal places.Part 4 of 8 -Question 10 of 17 1.0 PointsAccepted 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.xlsxTreating 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.Question 11 of 17 1.0 PointsAccepted 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.xlsxTreating 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.Part 5 of 8 -Question 12 of 17 1.0 PointsAccepted 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) wh

ere “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 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.Question 13 of 17 1.0 PointsAccepted 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 the test value you would use to conduct such a test of hypothesis?Place your answer, rounded to 2 decimal places, in the blank. For example, 2.34 would be a legitimate entry.Part 6 of 8 -Question 14 of 17 3.0 PointsAccepted 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 professor gives an exam for which there are two versions, A and B. Each student in the class is given one randomly selected version of the exam. After the exam, the professor wishes to determine if there is a difference in the level of difficulty of the two versions by determining if there is a significant difference in the mean scores. Assume ? = 0.05.Version A Version BSample size 45 65Mean score 8.8 8.2Sample variance 2.6 2.4What is the test value for this hypothesis test?Answer: Round your answer to two decimal places.What is/are the critical value(s) for this hypothesis test? If there are two critical values, give only the positive value.Answer: Round your answer to two decimal places.What is the conclusion for this hypothesis test? Choose one.1. There is not sufficient evidence to show that one version of the exam is more difficult than the other.2. There is sufficient evidence to show that one version of the exam is more difficult than the other.Answer: Enter only a 1 or 2 for your answer.Part 7 of 8 -Question 15 of 17 1.0 PointsWhen testing the equality of two population variances, the test statistic is the ratio of the population variances; namely .TrueFalsePart 8 of 8 -Question 16 of 17 1.0 PointsIn 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 â0.85.TrueFalseQuestion 17 of 17 1.0 PointsIn a simple linear regression problem, if the coefficient of determination is 0.95, this means that 95% of the variation in the explanatory variable X can be explained by regression.TrueFalse