# apu math302 quiz 5 done on may 2015

September 29, 2018

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:
three decimal places.

What is the critical value?

Critical value:
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.

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

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