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##### stats problems with solution fall 2014

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Question;Question 1 of 17 1.0;Points;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.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 40 70;Mean trunk diameter (cm) 45 39;Sample variance 100 150;A.The data support;the claim because the test value 2.78 is greater than 1.28.;B. The data do not;support the claim because the test value 1.29 is greater than 1.28.;C. The data support;the claim because the test value 2.78 is greater than 1.64.;D.The data do not;support the claim because the test value 1.29 is less than 1.64.;Question 2 of 17 1.0;Points;Members of the general adult population volunteer an average;of 4.2 hours per week. A random sample of 20 female college students and 18;male college students produced the results given in the table below. At the.01;level of significance, is there sufficient evidence to conclude that a;difference exists between the mean number of volunteer hours per week for male;and female college students?;Females Males;Sample size 20 18;Sample mean 3.8 2.5;Sample variance 3.5 2.2;A.No, because the;test value 2.38 is greater than the critical value;B.No, because the;test value 2.38 does not exceed the critical value;C.No, because the;test value 2.90 is greater than the critical value;D.Yes, because the;test value 2.90 is greater than the critical value;Question 3 of 17 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 blood and;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;Suppose you wanted to conduct a test of hypothesis to;determine if there is sufficient evidence to conclude that the mean bone marrow;microvessel density is higher before the stem cell transplant than after the;stem cell transplant? What is the;p-value associated with the test of hypothesis you would conduct?;A.p =.057493;B.p =.114986;C.p =.942597;D.p =.885014;Question 4 of 17 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 Apartments.xlsx.;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 5 of 17 1.0;Points;Outliers are observations that;A.disrupt the;entire linear trend;B.render the study;useless;C.lie outside the;typical pattern of points;D.lie outside the;sample;Question 6 of 17;The 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 6;Shelf Space 5 5 5 10 10 10;Weekly Sales 1.6 2.2 1.4 1.9 2.4 2.6;Store 7 8 9 10 11 12;Shelf Space 15 15 15 20 20 20;Weekly Sales 2.3 2.7 2.8 2.6 2.9 3.1;What is the estimated regression equation?;a. y^= 2.63 + 0.724x;b. y^= 1.45 + 0.724x;c. y^= 2.63 - 0.174x;d. y^= 1.45 + 0.074x;Question 7 of 17 1.0;Points;A correlation value of zero indicates.;A.a weak linear;relationship;B.a perfect linear;relationship;C.no linear;relationship;D.a strong linear;relationship;Question 8 of 17 1.0;Points;The regression line y' = -3 + 2.5 X has been fitted to the;data points (28, 60), (20, 50), (10, 18), and (25, 55). The sum of the squared;residuals will be;A.16.00;B.94.25;C.49.00;D.20.25;Question 9 of 17 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 20 30;Mean trunk diameter (cm) 45 39;Sample variance 100 150;What 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.;Question 10 of 17 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.;a =;b =;Question 11 of 17 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;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 would be a legitimate;entry.;Part 5 of 8 -;Question 12 of 17 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 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;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.;Q-Mart is interested in comparing its male and female customers.;Q-Mart would like to know if the amount of money spent by its female charge;customers differs, on average, from the amount spent by its male charge;customers.;To answer this question, an analyst collected random samples;of 25 female customers and 22 male customers. Based on these samples, on;average, the 25 women charge customers spent $102.23 and the 22 men charge;customers spent $86.46. Moreover, the sample standard deviation of the amount;charged by the 25 women was $93.393, and the sample standard deviation of the;amount charged by the 22 men was $59.695.;Suppose, using a 10% level of significance, you wish to know;if there is sufficient evidence for Q-Mart to conclude that, on average, the;amount spent by women charge customers differs from the amount spent by men;charge customers. That is suppose you wish to test;H0: versus H1;Assuming that the amounts spent by female and male charge;customers at Q-Mart are normally distributed, based on the procedure advocated;by Bluman, what is/are the critical values that you would use to conduct this;test of hypothesis? Place your answer, rounded to 3 decimal places, in the;blank. If there are two critical values, place only the positive value in the;blank. For example, 2.035 would be a legitimate entry.;Question 14 of 17 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 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 B;Sample size 45 65;Mean score 8.8 8.2;Sample variance 2.6 2.4;What 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.;Question 15 of 17 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;Question 16 of 17 1.0;Points;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;Question 17 of 17 1.0;Points;If there is no linear relationship between two variables X;and Y, the coefficient of determination, R2, must be 1.0.;True;False

Paper#61572 | Written in 18-Jul-2015

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