maths homework assignment-Two independent samples of sizes n1 = 50 and n2 = 50 are randomly selected from two

Part
1 of 8 –

Question 1 of 17

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,.gif” alt=”f$mu_{1}-mu _{2}f$ “> . The sampling
distribution of the sample mean difference,.gif” alt=”f$ar{X_{1}}-ar{X_{2}}f$ “> is:

A.t
– distributed with 98 degrees of freedom

B.chi-squared
distributed with 99 degrees of freedom

C.normally
distributed

D.approximately
normal

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Question 2 of 17

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
= 3.252

B.t
= 0.151

C.z
= 0.455

D.z
= 0.081

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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

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.t
= 1.8424

C.z
= 1.8424

D.t
= 2.7234

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Part
2 of 8 –

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.

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At the .05 level of significance determine if the correlation between
rental cost and apartment size is significant.

A.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.

B.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.

C.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.

D.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.

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Question 5 of 17

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

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

A.0.684

B.0.308

C.0.652

D.0.827

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Question 6 of 17

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..gif” alt=”f$hat{y}f$ “> = 1.45 + 0.074x

B..gif” alt=”f$hat{y}f$ “> = 2.63 – 0.174x

C..gif” alt=”f$hat{y}f$ “> = 2.63 + 0.724x

D..gif” alt=”f$hat{y}f$ “> = 1.45 + 0.724x

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Question 7 of 17

1.0 Points

Correlation
is a summary measure that indicates:

A.a
curved relationship among the variables

B.the
magnitude of difference between two variables

C.the
rate of change in Y for a one unit change in X

D.the
strength of the linear relationship between pairs of variables

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Question 8 of 17

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.unknown

B.10

C.5

D.0

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Part
3 of 8 –

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

30

35

Mean trunk diameter (cm)

45

39

Sample variance

120

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 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

Find the equation of the regression line for these data. What is the value
of the coefficient of determination? Place your answer, rounded to 3
decimal places, in the blank. Do not use a dollar sign. For
example, 0.345 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.
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.

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 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.

Part
6 of 8 –

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 special coating is applied to several scale model engine nacelle body shapes
to determine if it reduces the drag coefficient. The following data
are the drag coefficient before the coating is applied and after.

Model

#1

#2

#3

#4

#5

#6

Before

0.782

0.656

0.541

0.250

0.323

0.888

After

0.668

0.581

0.532

0.241

0.334

0.891

Perform a hypothesis test to determine if there is evidence at the 0.05
level of significance to support the claim that the coating reduces the
drag coefficient.

What is the test value for this hypothesis test?

Answer: Round your answer to two decimal places.

What is the P-value for this hypothesis test?

Answer: Round your answer to three decimal places.

What is your conclusion for this test? Choose one.

1. There is sufficient evidence to show the coating reduces the drag
coefficient.
2. There is not sufficient evidence to show that the coating reduces
the drag coefficient.
3. There is sufficient evidence to show that the drag coefficient
changed after the coating was applied.
4. There is sufficient evidence to show that the drag coefficient
increased after the coating was applied.

Answer: Enter only a 1, 2, 3 or 4 for your answer.

Part
7 of 8 –

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.gif” alt=”f$ar{D}f$ “> ; the sample mean
difference between the pairs.

True

False

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Part
8 of 8 –

Question 16 of 17

1.0 Points

To
help explain or predict the response variable in every regression study, we
use one or more explanatory variables. These variables are also called
predictor variables or independent variables.

True

False

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Question 17 of 17

1.0 Points

When
the actual values y of a response variable and the corresponding
predicted values y’ are the same, the standard error of the estimate will
be zero.

True

False

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