# apu math302 final exam done on may 2015

September 29, 2018

Question 1 of 23 1.0/
1.0 Points
A company operates four machines during three shifts each
day. From production records, the data in the table below were collected. At
the .05 level of significance test to determine if the number of breakdowns is
independent of the shift.

Machine
Shift A B C D
1 41 20 12 16
2 31 11 9 14
3 15 17 16 10

A.The number of breakdowns is dependent on
the shift, because the test value 11.649 is less than the critical value of
12.592.

B.The claim that the number of breakdowns is independent of the shift
cannot be rejected, because the test value 11.649 is less than the critical
value of 12.592.
C.The number of breakdowns is dependent on
the shift, because the p-value is .07.

D.The number of breakdowns is independent of
the shift, because the test value 12.592 is greater than the critical value of 11.649.

Question 2 of 23 1.0/
1.0 Points
The data presented in the table below resulted from an
experiment in which seeds of 5 different types were planted and the number of
seeds that germinated within 5 weeks after planting was recorded for each seed
type. At the .01 level of significance, is the proportion of seeds that
germinate dependent on the seed type?

Seed Type Observed Frequencies
Germinated Failed to Germinate
1 31 7
2 57 33
3 87 60
4 52 44
5 10 19

A.Yes, because the test value 16.86 is greater than the critical value
of 13.28

B.Yes, because the test value 16.86 is less
than the critical value of 14.86

C.No, because the test value 16.86 is greater
than the critical value of 13.28

D.No, because the test value 13.28 is less
than the critical value of 16.86

Part 2 of 16 – 3.0/
3.0 Points

Question 3 of 23 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.25%

B.80%

C.50%

D.20%

Question 4 of 23 1.0/
1.0 Points
In regression analysis, the variable we are trying to
explain or predict is called the

A.dependent variable

B.independent variable
C.regression variable

D.residual variable

Question 5 of 23 1.0/
1.0 Points
In choosing the “best-fitting” line through a set of points
in linear regression, we choose the one with the:

A.smallest sum of squared residuals

B.largest number of points on the line

C.smallest number of outliers

D.largest sum of squared residuals

Part 3 of 16 – 2.0/
2.0 Points

Question 6 of 23 1.0/
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.t = 2.7234

B.p = 2.7234

C.z = 1.8424

D.t = 1.8424

Question 7 of 23 1.0/
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

Suppose you wanted to conduct a test of hypothesis to
determine if there is sufficient evidence to conclude that the mean bone marrow
microvessel density is higher before the stem cell transplant than after the
stem cell transplant? What is the
p-value associated with the test of hypothesis you would conduct?

A.p = .942597

B.p = .057493

C.p = .114986

D.p = .885014

Part 4 of 16 – 2.0/
3.0 Points

Question 8 of 23 0.0/
1.0 Points
A lab technician is
tested for her consistency by taking multiple measurements of cholesterol
levels from the same blood sample. The target accuracy is a variance in
measurements of 1.2 or less. If the lab technician takes 16 measurements and
the variance of the measurements in the sample is 2.2, does this provide enough
evidence to reject the claim that the lab technician’s accuracy is within the
target accuracy?

At the ? = .01 level of significance, what is your
conclusion?

A.Do not reject H0. At the = .01 level of significance there is not
sufficient evidence to suggest that this technician’s true variance is greater
than the target accuracy.
B.Reject H0. At the = .01 level of significance, there is enough
evidence to support the claim that this technician’s variance is larger than
the target accuracy.
C.Cannot determine

D.
Reject
H0. At the = .01 level of significance, there is not
enough evidence to support the claim that this technician’s true variance is
larger than the target accuracy.

Question 9 of 23 1.0/
1.0 Points
A null hypothesis can only be rejected at the 5%
significance level if and only if:

A.a 95% confidence interval includes the
hypothesized value of the parameter

B.a 95% confidence interval does not include the hypothesized value of
the parameter
C.the null hypotheses includes sampling error

D.the null hypothesis is biased

Question 10 of 23 1.0/
1.0 Points
In an article appearing in Today’s Health a writer states
that the average number of calories in a serving of popcorn is 75. To determine
if the average number of calories in a serving of popcorn is different from 75,
a nutritionist selected a random sample of 20 servings of popcorn and computed
the sample mean number of calories per serving to be 78 with a sample standard
deviation of 7.

At the ? = .05 level of significance, does the nutritionist
have enough evidence to reject the writer’s claim?

A.Yes

B.No

C.Cannot Determine

Part 5 of 16 – 2.0/
2.0 Points

Question 11 of 23 1.0/
1.0 Points
The t- distribution for developing a confidence interval for
a mean has _____ degrees of freedom.

A.n + 1

B.n – 1

C.n

D.n – 2

Question 12 of 23 1.0/
1.0 Points
In order to be
accepted into a top university, applicants must score within the top 5% on the
SAT exam. Given that SAT test scores are normally distributed with a mean of
1000 and a standard deviation of 200, what is the lowest possible score a
student needs to qualify for acceptance into the university?

A.1330

B.1400

C.1250

D.1100

Part 6 of 16 – 1.0/
1.0 Points

Question 13 of 23 1.0/
1.0 Points
If the value of the standard normal random variable Z is
positive, then the original score is where in relationship to the mean?

A.equal to the mean

B.to the left of the mean

C.to the right of the mean

D.one standard deviation higher than the mean

Part 7 of 16 – 1.0/
1.0 Points

Question 14 of 23 1.0/
1.0 Points
In a small town, 60% of the households have dogs. If 5
households are randomly selected, what is the probability that at least 4 of
them have dogs?

A.0.337

B.3

C.0.8

D.0.259

Part 8 of 16 – 1.0/
1.0 Points

Question 15 of 23 1.0/
1.0 Points
If events A and B are mutually exclusive, then the
probability of both events occurring simultaneously is equal to

A.0.0

B.1.0

C.0.5

D.any value between 0.5 and 1.0

Part 9 of 16 – 3.0/
3.0 Points

Question 16 of 23 3.0/
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 sport preference poll yielded the following data for men
and women. Use a 5% significance level and test to determine if sport
preference and gender are independent.
Sport Preferences of Men and Women
Men 20 25 30 75
Women 18 12 15 45
38 37 45 120

What is the test value for this hypothesis test?

What is the critical value for this hypothesis test?

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

1. There is
sufficient evidence to support the claim that one’s sport preference is
dependent on one’s gender.
2. There is not sufficient evidence to support the claim
that one’s sport preference is dependent on one’s gender.

Part 10 of 16 – 1.0/
1.0 Points

Question 17 of 23 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.
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.

blank. Do not use a dollar sign. For example, 2.345 would be a legitimate
entry. 2.442

Part 11 of 16 – 0.0/
1.0 Points

Question 18 of 23 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.

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?

blank. For example, .0123 would be a legitimate entry. 1.18

Part 12 of 16 – 1.0/
1.0 Points

Question 19 of 23 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.
In a particular region of Cape Cod, it is known that
lobstermen trap on average of 32 pounds of lobster per day with a standard
deviation of four pounds. If a random sample of 30 lobster fishermen is
selected, what is the probability that their average catch is less than 31.5
pounds?

blank. 0.2468
When entering your answer do not use any labels or symbols other than a
decimal point. Simply provide the numerical value. For example, 0.1234 would be
a legitimate entry.

Part 13 of 16 – 0.0/
1.0 Points

Question 20 of 23 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.

The personnel department of a large corporation wants to
estimate the family dental expenses of its employees to determine the
feasibility of providing a dental insurance plan. A random sample of 12
employees reveals the following family dental expenses (in dollars): 115, 370,
250, 593, 540, 225, 177, 425, 318, 182, 275, and 228.

Construct a 99% confidence interval estimate for the
standard deviation of family dental expenses for all employees of this
corporation.

Place your LOWER limit, in dollars rounded to 1 decimal
place, in the first blank. Do not use a dollar sign, a comma, or any other
stray mark. For example, 98.4 would be a legitimate entry. 175.5

Place your UPPER limit, in dollars rounded to 1 decimal
place, in the second blank. Do not use a dollar sign, a comma, or any other
stray mark. For example, 567.8 would be a legitimate entry. 440.8

Part 14 of 16 – 1.0/
1.0 Points

Question 21 of 23 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 school determines that the number of children X in the
families who attend the school follows the distribution below:
Number of children X 1 2
3 4 5
Probability P(X) 0.20 0.35 0.25 0.15
0.05

What is the mean number of children per family? Round your answer to one decimal place as
necessary. For example, 4.5 would be a legitimate entry.

Part 15 of 16 – 1.0/
1.0 Points

Question 22 of 23 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.

The ABC battery company claims that their batteries last at
least 100 hours, on average. Your experience with their batteries has been
somewhat different, so you decide to conduct a test to see if the company’s
claim is true. You believe that the mean life is actually less than the 100
hours the company claims. You decide to collect data on the average battery
life (in hours) of a random sample of n = 20 batteries. Some of the information
related to the hypothesis test is presented below.

Test of H0: 100
versus H1: 100
Sample mean 98.5
Std error of mean 0.777

Assuming the life length of batteries is normally
distributed, what is the p-value associated with this test? Place your answer,
rounded to 3 decimal places in the blank. For example, 0.234 would be a
legitimate entry. 0.0343

Part 16 of 16 – 1.0/
1.0 Points

Question 23 of 23 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.

Suppose that a marketing firm sends questionnaires to two
different companies. Based on historical evidence, the marketing research firm
believes that each company, independently of the other, will return the
questionnaire with a probability of 0.30. What is the probability that both