# apu math302 final exam done on may 2015

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

Basketball Football Soccer

Men 20 25 30 75

Women 18 12 15 45

38 37 45 120

What is the test value for this hypothesis test?

Round your answer to two decimal places.

What is the critical value for this hypothesis test?

Round your answer to two decimal places.

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.

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. 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?

Place your answer, rounded to 4 decimal places, in the

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?

Place your answer, rounded to four decimal places, in the

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

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

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

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

questionnaires will be returned? Place your answer, rounded to 2 decimal

places, in the blank. For example, 0.23 is a legitimate entry. 0.09

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