Homework #11 Chapter 11

WebAssignHomework #11 Chapter 11 (Homework)

Long NguyenMath 10, section 12, Winter 2011Instructor: Roberta Bloom

Current Score : 10 / 10 Due : Friday, March 18, 2011 11:00 AM PDT

Homework #11 Chapter 11 http://www.webassign.net/v4cginguyen.long@deanza/student.p...

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1. 1.4/1.4 points Question: IDCollabStat1 11.HW.002.

A 6-sided die is rolled 120 times. Fill in the expected frequency column. Then, conduct a hypothesis test at the 5%

level to determine if the die is fair. The data below are the result of the 120 rolls.

Face Value Frequency Expected Frequency

1 14 20

2 31 20

3 15 20

4 15 20

5 30 20

6 15 20

Part (a)

Part (b)

Part (c)

Part (d)

Part (e)

Part (f)

State the null hypothesis.

The data do not fit the distribution for a fair 6-sided die.

The data fit the distribution for a fair 6-sided die.

State the alternative hypothesis.

The data fit the distribution for a fair 6-sided die.

The data do not fit the distribution for a fair 6-sided die.

What are the degrees of freedom?

5

State the distribution to use for the test.

t6

t5

What is the test statistic? (Round your answer to two decimal places.)

16.6


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Part (g)

Part (h)


What is the p-value? (Round your answer to four decimal places.)

0.0053

Explain what the p-value means for this problem.

Correct! A p-value is the probability that an outcome of the data will happen purely by chance when is

true.

If is false, then there is a chance equal to the p-value that the value of the test statistic

will be equal to or greater than the calculated value.

If is true, then there is a chance equal to the p-value that the value of the test statistic

will be equal to or less than the calculated value.





H0

H0

H0

H0

H0

Sketch a picture of this situation. Label and scale the horizontal axis, and shade the region(s) corresponding

to the p-value. (Upload your file below.)

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Indicate the correct decision ("reject" or "do not reject" the null hypothesis) and write the appropriate

conclusion.

(i) Alpha:

α = 0.05

(ii) Decision:

(iii) Reason for decision:

(iv) Conclusion:

reject the null hypothesis

do not reject the null hypothesis

Since α < p-value, we do not reject the null hypothesis.

Since α > p-value, we do not reject the null hypothesis.

Since α > p-value, we reject the null hypothesis.

Since α < p-value, we reject the null hypothesis.

There is sufficient evidence to conclude that the data do not fit the distribution for a fair

6-sided die.

There is not sufficient evidence to conclude that the data do not fit the distribution for a

fair 6-sided die.


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The marital status distribution of the U.S. male population, age 15 and older, is as shown below.

Marital Status Percent

never married 31.3

married 56.1

widowed 2.5

divorced/separated 10.1

Suppose that a random sample of 400 U.S. young adult males, 18 – 24 years old, yielded the following frequency

distribution. We are interested in whether this age group of males fits the distribution of the U.S. adult population

at the 5% level. Calculate the frequency one would expect when surveying 400 people. Fill in the table below,

rounding to two decimal places.

Marital Status Frequency Expected Frequency

never married 138 125.20

married 239 224.4

widowed 2 10

divorced/separated 21 40.4

Part (a)

Part (b)

Part (c)

Part (d)


The data fit the distribution of marital status for the U.S. adult population.

The data do not fit the distribution of marital status for the U.S. adult population.


The data do not fit the distribution of marital status for the U.S. adult population.

The data fit the distribution of marital status for the U.S. adult population.


3


t3

t4


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Part (e)

Part (f)

Part (g)

Part (h)



17.97


0.0004



true.









H0

H0

H0

H0

H0



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conclusion.

(i) Alpha:

α = 0.05

(ii) Decision:


(iv) Conclusion:







There is sufficient evidence to conclude that the data do not fit the distribution of marital

status for the U.S. adult population.

There is not sufficient evidence to conclude that the data do not fit the distribution of

marital status for the U.S. adult population.


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The City of South Lake Tahoe has an Asian population of 1419 people, out of a total population of 23,609.†

Conduct a goodness of fit test at the 5% level to determine if the self-reported sub-groups of Asians are evenly

distributed. (Round expected frequency to two decimal places.)

Race Frequency Expected Frequency

Asian Indian 131 202.71

Chinese 118 202.71

Filipino 1045 202.71

Japanese 80 202.71

Korean 12 202.71

Vietnamese 9 202.71

Other 24 202.71

Part (a)

Part (b)

Part (c)

Part (d)

Part (e)


The self-reported sub-groups of Asians are not evenly distributed.

The self-reported sub-groups of Asians are evenly distributed.


The self-reported sub-groups of Asians are evenly distributed.

The self-reported sub-groups of Asians are not evenly distributed.


6


t6

t7


4156.97


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Part (f)

Part (g)

Part (h)



0.0000



true.









H0

H0

H0

H0

H0



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conclusion.

(i) Alpha:

α = 0.05

(ii) Decision:


(iv) Conclusion:







There is sufficient evidence to conclude that the self-reported sub-groups of Asians are

not evenly distributed.

There is not sufficient evidence to conclude that the self-reported sub-groups of Asians

are not evenly distributed.


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Car manufacturers are interested in whether there is a relationship between the size of car an individual drives

and the number of people in the driver's family (that is, whether car size and family size are independent). To test

this, suppose that 801 car owners were randomly surveyed with the following results. Conduct a test for

independence at the 5% level.

Family Size Sub & Compact Mid-size Full-size Van & Truck

1 19 34 41 36

2 19 50 69 79

3 - 4 20 50 100 91

5+ 20 31 71 71

Part (a)

Part (b)

Part (c)

Part (d)

Part (e)

Part (f)


The size of the car an individual drives is dependent on the number of people in the driver's

family.

The size of the car an individual drives is independent of the number of people in the driver's

family.


The size of the car an individual drives is independent of the number of people in the driver's

family.

The size of the car an individual drives is dependent on the number of people in the driver's

family.


9


t9

t3


13.73


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Part (g)

Part (h)



0.1322



true.









H0

H0

H0

H0

H0



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conclusion.

(i) Alpha:

α = 0.05

(ii) Decision:


(iv) Conclusion:







There is sufficient evidence to conclude that the size of the car an individual drives is

dependent on the number of people in the driver's family.

There is not sufficient evidence to conclude that the size of the car an individual drives is

dependent on the number of people in the driver's family.


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Some travel agents claim that honeymoon hot spots vary according to the age of the bride and groom. Suppose

that 283 East Coast recent brides were interviewed as to where they spent their honeymoons. The information is

given below. Conduct a test for independence at the 5% level.

Location 20 – 29 30 – 39 40 – 49 50 and over

Niagara Falls 14 26 24 20

Poconos 15 25 26 11

Europe 10 24 14 6

Virgin Islands 21 25 16 6

Part (a)

Part (b)

Part (c)

Part (d)

Part (e)

Part (f)


The honeymoon location is dependent on the age of the bride and groom.

The honeymoon location is independent of the age of the bride and groom.


The honeymoon location is dependent on the age of the bride and groom.

The honeymoon location is independent of the age of the bride and groom.


9


t3

t9


14.08


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Part (g)

Part (h)



0.1195



true.









H0

H0

H0

H0

H0



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conclusion.

(i) Alpha:

α = 0.05

(ii) Decision:


(iv) Conclusion:







There is sufficient evidence to conclude that the honeymoon location is dependent on

the age of the bride and groom.

There is not sufficient evidence to conclude that the honeymoon location is dependent

on the age of the bride and groom.


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A manager of a sports club keeps information concerning the main sport in which members participate and their

ages. To test whether there is a relationship between the age of a member and his or her choice of sport, 635

members of the sports club are randomly selected. Conduct a test for independence at the 5% level.

Sport 18 – 25 26 – 30 31 – 40 41 and over

racquetball 41 56 29 44

tennis 59 75 38 64

swimming 73 59 64 33

Part (a)

Part (b)

Part (c)

Part (d)

Part (e)

Part (f)


An individual's choice of sport is dependent on age.

An individual's choice of sport is independent of age.


An individual's choice of sport is independent of age.

An individual's choice of sport is dependent on age.


6


t6

t3


24.17


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Part (g)

Part (h)



0.0004



true.









H0

H0

H0

H0

H0



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conclusion.

(i) Alpha:

α = 0.05

(ii) Decision:


(iv) Conclusion:







There is sufficient evidence to conclude that an individual's sport of choice is dependent

on age.

There is not sufficient evidence to conclude that an individual's sport of choice is

dependent on age.


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Suppose that 600 30-year-olds were surveyed to determine whether or not there is a relationship between the

level of education an individual has and salary. Conduct a test for independence at the 5% level.

Annual SalaryNot a high school

graduate

High school

graduateCollege graduate Masters or doctorate

< $30,000 15 25 15 5

$30,000 – $40,000 25 45 70 30

$40,000 – $50,000 10 0 35 55

$50,000 – $60,000 5 15 15 60

$60,000+ 5 10 15 145

Part (a)

Part (b)

Part (c)

Part (d)

Part (e)


The annual salary of the 30-year-old is dependent on the level of education that the individual

obtained.

The annual salary of the 30-year-old is independent of the level of education that the individual

obtained.


The annual salary of the 30-year-old is independent of the level of education that the individual

obtained.

The annual salary of the 30-year-old is dependent on the level of education that the individual

obtained.


12


t12

t5


236.40


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Part (f)

Part (g)

Part (h)


0.0000



true.









H0

H0

H0

H0

H0



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conclusion.

(i) Alpha:

α = 0.05

(ii) Decision:


(iv) Conclusion:







There is sufficient evidence to conclude that the annual salary of the 30-year-old is

dependent on the level of education that the individual obtained.

There is not sufficient evidence to conclude that the annual salary of the 30-year-old is

dependent on the level of education that the individual obtained.


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Homework #11 Chapter 11

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