MATH302 QUIZ 5

Question # 00021861 Posted By: spqr Updated on: 08/03/2014 07:05 AM Due on: 09/21/2014
Subject Mathematics Topic General Mathematics Tutorials:
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Question 1 of 17 0.0/ 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 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/ 1.0 Points

A 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.7.03

B.49.50

C.9.61

D.3.10

Question 3 of 17 1.0/ 1.0 Points

Some 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?

Plea

Guilty Not Guilty

Number judged guilty n1 = 191 n2 = 64

Number sentenced to prison x1 = 101 x2 = 56

Sample proportion .529 .875

A.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 - 5.0/ 5.0 Points




Question 4 of 17 1.0/ 1.0 Points

The standard error of the estimate, sest, is essentially the

A.mean of the residuals

B.standard deviation of the residuals

C.standard deviation of the explanatory variable

D.mean of the explanatory variable

Question 5 of 17 1.0/ 1.0 Points

In a simple linear regression analysis, the following sum of squares are produced:

= 500

= 100

= 400

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/ 1.0 Points

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. = 2.63 - 0.174x

B. = 1.45 + 0.074x

C. = 1.45 + 0.724x

D. = 2.63 + 0.724x





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.mutually exclusive

B.inversely related

C.highly correlated

D.directly related




Question 8 of 17 1.0/ 1.0 Points

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

Is 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 - 0.0/ 2.0 Points




Question 9 of 17 0.0/ 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 25 35

Mean trunk diameter (cm) 55 48

Sample variance 100 140

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:






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.

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



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.

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. 525.4





Part 5 of 8 - 2.0/ 2.0 Points

Question 12 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 the p-value associated with such a test of hypothesis?


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 the test value you would use to conduct such a test of hypothesis?







Part 6 of 8 - 1.0/ 3.0 Points

Question 14 of 17 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 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?







What is/are the critical value(s) for this hypothesis test? If there are two critical values, give only the positive value.




What is the conclusion for this hypothesis test? Choose one.

1







Part 7 of 8 - 1.0/ 1.0 Points

Question 15 of 17 1.0/ 1.0 Points

When testing the equality of two population variances, the test statistic is the ratio of the population variances; namely .

True

False

Part 8 of 8 - 2.0/ 2.0 Points

Question 16 of 17 1.0/ 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/ 1.0 Points

In 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.

True

False

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Tutorials for this Question
  1. Tutorial # 00021211 Posted By: spqr Posted on: 08/03/2014 07:06 AM
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    food. For a random sample of 12 similar stores, she gathered ...
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