# apu math302 quiz 5 done on may 2015

Question 1 of 17

1.0/ 1.0 Points

Two independent samples of sizes n1 = 50 and n2 = 50 are

randomly selected from two populations to test the difference between the

population means, f$mu_{1}-mu _{2}f$ .

The sampling distribution of the sample mean difference, f$ar{X_{1}}-ar{X_{2}}f$ is:

A.approximately

normal

B.chi-squared

distributed with 99 degrees of freedom

C.t – distributed

with 98 degrees of freedom

D.normally

distributed

Question 2 of 17

0.0/ 1.0 Points

A pharmaceutical company is testing the effectiveness of a

new drug for lowering cholesterol. As part of this trial, they wish to

determine whether there is a difference between the effectiveness for women and

for men. Assume ? = 0.05. What is the test value?

Women

Men

Sample size

50

80

Mean effect

7

6.95

Sample variance

3

4

A.t = 0.151

B.z =

0.081

C.z = 0.455

D.t = 3.252

Feedback: This is a t-test of independent samples. To compue

the test value t use:

f[t=frac{(7-6.95)-0}{sqrt{frac{3}{50}+frac{4}{80}}}=0.150756f]

Question 3 of 17

1.0/ 1.0 Points

Which of the following statements is true regarding the F –

distribution?

A.It is a

distribution of negative values

B.It is always skewed

to the left

C.It typically

appears in tests of equal proportions

D.none of the above

Part 2 of 8 – 3.0/

5.0 Points

Question 4 of 17

1.0/ 1.0 Points

The correlation value ranges from

A.-3 to +3

B.–1 to +1

C.0 to +1

D.–2 to +2

Question 5 of 17

1.0/ 1.0 Points

Data for a

sample of 25 apartments in a particular neighborhood are provided in the

worksheet Apartments in the Excel workbook Apartments.xlsx. Using that data, find the estimated

regression equation which can be used to estimate the monthly rent for

apartments in this neighborhood using size as the predictor variable.

Apartments.xlsx

A. f$hat{y}= f$ 177.12 + 1.065(size)

B.f$hat{y}= f$

1.065 + 177.12(size)

C.f$hat{y}= f$

177.12 + 0.8500(size)

D.f$hat{y}= f$

197.12 + 2.065(size)

Question 6 of 17

0.0/ 1.0 Points

If an estimated regression line has a Y-intercept of –7.5

and a slope of 2.5, then when X = 3, the actual value of Y is:

A.5

B.10

In C.0

D.unknown

Question 7 of 17

0.0/ 1.0 Points

Outliers are observations that

A.disrupt the entire

linear trend

B.render the study

useless

In C.lie outside the sample

D.lie outside the

typical pattern of points

Question 8 of 17

1.0/ 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.

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 sample correlation coefficient 0.85 exceeds 0.50.

B.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.

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.

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

30

35

Mean trunk diameter (cm)

45

39

Sample variance

120

140

What is the test value for this hypothesis test?

Test value:

Correct2.474 Round your answer to

three decimal places.

What is the critical value?

Critical value:

Correct1.296 Round your answer to

three decimal places.

Feedback: This is a t-test of independent samples. Use the formula for the t test value on page

480:

f[t=frac{(45-39)-0}{sqrt{frac{120}{30}+frac{140}{35}}}=2.121320f]

Using Table F (df = 29, alpha = 0.10, one-tail test) the

critical t-value is 1.311.

Part 4 of 8 – 2.0/

2.0 Points

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.

Data for a sample of 25 apartments in a particular

neighborhood are provided in the worksheet Apartments in the Excel workbook

Apartments.xlsx. Using the estimated regression equation found by using size as

the predictor variable, find a point estimate for the average monthly rent for

apartments having 1,000 square feet of space. Place your answer, rounded to the

nearest whole dollar, in the blank.

Correct1242 When entering your

answer do not use any labels or symbols. Simply provide the numerical value. For

example, 123 would be a legitimate entry.

Apartments.xlsx

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.

Correct525.4

Part 5 of 8 – 0.0/

2.0 Points

Question 12 of 17

0.0/ 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.

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 test value

that you would use to conduct this test of hypothesis? Place your answer, rounded to 3 decimal

places, in the blank. For example, 2.345

would be a legitimate entry.

Correct0.357

Question 13 of 17

0.0/ 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.

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 critical

value that you would use to conduct this test of hypothesis? Place your answer,

rounded to 3 decimal places, in the blank. For example, 2.345 would be a

legitimate entry. Correct1.773

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. 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.

Part 7 of 8 – 1.0/

1.0 Points

Question 15 of 17

1.0/ 1.0 Points

In conducting hypothesis testing for difference between two

means when samples are dependent (paired samples), the variable under

consideration is f$ar{D}f$ ; the

sample mean difference between the pairs.

Correct

True

False

Part 8 of 8 – 2.0/

2.0 Points

Question 16 of 17

1.0/ 1.0 Points

In a simple regression analysis, if the standard error of

estimate sest = 15 and the number of observations n = 10, then the sum of the

residuals squared must be 120.

True

False

Question 17 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