Solution-Compute the value of the sample correlation

Compute the value of the sample correlation coefficient

Assignment Help Basic Statistics

Reference no: EM13920853

Question 1

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.Yes, because the test value 2.58 is inside the interval (-4.94, 4.94)

C.Yes, because the test value -4.94 is outside the interval (-2.58, 2.58)

D.No, because the test value -4.94 is outside the interval (-1.96, 1.96)

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Question 2

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

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.p = 2.7234

B.z = 1.8424

C.t = 2.7234

D.t = 1.8424

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Question 3

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.9.61

B.7.03

C.3.10

D.49.50

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Part 2 of 8 -

Question 4

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

Compute the value of the sample correlation coefficient between weekly sales and shelf space.

A.0.827

B.0.652

C.0.684

D.0.308

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Question 5

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.80%

B.50%

C.20%

D.25%

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Question 6

The city of Oakdale wishes to see if there is a linear relationship between the temperature and the amount of electricity used (in kilowatts).

Based on the data in the table below, is there a significant linear relationship between temperature and the amount of electricity used?

These data are also available in the worksheet temperature in the Excel workbook Temperature.xlsx.
Temperature.xlsx

Temperature (x) 73 78 85 98 93 81 76 105

Kilowatts (y) 680 760 910 1510 1170 837 600 1800

A.No, the sample correlation coefficient is equal to 0.981, which does not provide evidence of a significant linear relationship.

B.Yes, the sample correlation coefficient is equal to 0.878, which provides evidence of a significant linear relationship.

C.Yes, the sample correlation coefficient is equal to 0.981, which provides evidence of a significant linear relationship.

D.No, the sample correlation coefficient is equal to 0.098, which does not provide evidence of a significant linear relationship.

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Question 7

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.50%

C.20%

D.25%

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Question 8

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

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Part 3 of 8 -

Question 9

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?

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

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.

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.

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.

Part 5 of 8 -

Question 12

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 p-value associated with this test of hypothesis?

Place your answer, rounded to 3 decimal places, in the blank.

For example, 0.134 would be a legitimate entry.

Question 13