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PAGE 1 1 Population assumption: Normal n =...

PAGE 1

1

Population assumption: Normal

n = 16; x = 96; s = 13;

H0: μ ≤ 84, H1: μ > 84;

α = 0.01

State the conclusion:

_________________

2

A simple random sample of 10 students is selected from a large college. For the 10

students, the number of days each was absent during the last semester was to be

1, 2, 9, 4, 1, 2, 3, 1, 4, and 4

What is the point estimate for σ, the variance of the number of days absent for the

college’s students? (Round your answer(s) to 3 decimal places.)

σ = _________

3

Population assumption: None

n = 40

x = 5

σ = 3.04

H0: μ ≤ 6.5

H1: μ > 6.5

α = 0.025. (Round your answer(s) to 3 decimal places.)

z = ______

State the conclusion:

_________________

4

The output from a process is normally distributed with a known standard deviation, but

the mean is unknown. 22 different simple random samples, each with n = 9, are to be

drawn from the process, and a 95% confidence interval for the mean is to be

constructed for each sample. What is the probability that at least 19 of the confidence

intervals will actually contain the population mean? Round your answer to the nearest

percent.

________ %

PAGE 2

5

A large bank in a metropolitan area has a large number of secured loans on apartment

facilities throughout the area. Local economic indicators suggest the percentage of

vacant apartments ranges from 6% to 11%. Concerned about the borrowers’ ability to

meet loan obligations on time the bank decides to sample from the apartments used to

secure loans. The officer responsible for the sample decides to allow a maximum error

of the estimate of 0.01 with 99 percent confidence. The officer wishes to take a sample

large enough to cover all proportions within the estimated vacancy range. Compute the

sample size needed for this study. (Round your answer(s) to 3 decimal places.)

_________

6

Use the information given to find the lower and upper critical values for the sample

mean:n = 973

σ = 43.53

μ = 447.3

α = 0.10 (Round your answer(s) to 3 decimal places.)

Lower value = _________

Upper value = _________

7

n = 400;

p-hat = 0.060;

H0: p ≥ 0.05,

H1: p < 0.05;

α = 0.01

Compute the test statistic. (Round your answer(s) to 3 decimal places.)

Appropriate test: _________________

Test statistic = _________

PAGE 3

8

Determine the p-value associated with each of the following values of the standardized

test statistic z. (Round your answer(s) to 3 decimal places.)

A) Two-tail test, with z = 1.5

p-value = _________

B) One-tail test, with z = 1.05

p-value = _________

C) One-tail test, with z = -1.15

p-value = _________

9

An airline, in response to passenger concern, conducts realistic tests to determine the

time needed to evacuate a Boeing 737. Average evacuation time in the past has been

100 seconds with a standard deviation of 15 seconds. The FFA requires tests that

show a planeload of passengers can be evacuated in 97 seconds. If the airline

conducts a sample of 30 tests, what is the probability that the average evacuation time

will be 97 seconds or less? (Round your answer(s) to 3 decimal places.)

P(x-bar ≤ 97) = _________

10

Find the chi-square value for each of the right-tail areas below, given that the degrees

of freedom are 8: (Round your answer(s) to 3 decimal places.)

A) 0.95, Χ2 = _________

B) 0.01 Χ2 = _________

C) 0.025 Χ2 = _________

D) 0.05 Χ2 = _________

PAGE 4

11

The owner of a video store is interested in whether or not there is a difference in the

proportions of VCR movies rented by members and non-members among movie titles.

Three movies are selected and each person who rents them is identified as a member

or non-member. A total of 350 people rent these movies and the responses are:

(Round your answer(s) to 3 decimal places.)

Cross Classification Table:

-------------------------------------------------------------------------------------

[ Movie ]

-------------------------------------------------------------------------------------

| Membership | Witness | Rambo | Karate Kid | Total |

-------------------------------------------------------------------------------------

| Member | 16 | 17 | 72 | 105 |

-------------------------------------------------------------------------------------

| Non-member | 84 | 83 | 78 | 245 |

-------------------------------------------------------------------------------------

| Total | 100 | 100 | 150 | 350 |

-------------------------------------------------------------------------------------

If Table gets all weird: cross classification table by rows:

Table Name: Movie

Row 1: Membership, with 4-Columns: Witness, Rambo, Karate Kid, Total

Row 2: Member, 16, 17, 72, 105

Row 3: Non-member, 84, 83, 78, 245

Row 4: Total, 100, 100, 150, 350

Answer the following:

a. What are the degrees of freedom for the test of equal proportions?

______

b. What is the expected frequency of the cell Rambo and Non-member?

_______________

c. What is the computed value of the test statistic?

Χ2 = _______________

d. What is the critical value for a 0.01 significance level?

_______________

e. What is the conclusion?

_________________

12

Cement for building a dam is delivered by truck. The dispatcher wants to estimate the

average driver time required to load, drive to the dam, unload, and drive back to the

plant. The time is assumed to be normally distributed. Total time required is recorded

for a random sample of 18 with a mean of 546.56 and a standard deviation of 85.53.

Use these data to obtain an 80-percent confidence interval for the average driver time.

(Round your answer(s) to 3 decimal places.)

80% CI = _________ to _________

PAGE 5

13

Raising in-state and out-of-state tuition is supposed to reduce the number of students

in state supported universities. The registrar of a university wants to estimate the

proportion, π, of students who are paying out-of-state tuition on the installment plan (to

later be compared with in-state installment plan payers). A random sample of 90

students who live out-of-state is taken and 39 of them pay tuition on the installment

plan. Find a 99-percent confidence interval for π based on these data. (Round your

answer(s) to 3 decimal places.)

99% CI = _________ to _________

14

A population consisted of 700 cases involving shoplifters. If a random sample of 250

was taken and in 75 cases the offender was under age 18, in how many of the 700

cases would you say the person involved was under age 18? (Round your answer(s) to

3 decimal places.)

Shoplifters (under 18) = _________ cases

(round your answer up to the nearest integer).

15

Determine the limits of the 85% confidence interval for p, given that n = 70; and p-hat =

0.35. (Round your answer(s) to 3 decimal places.)

85% CI = _________ to _________

16

My daughter and I have argued about the average length of our preacher’s sermons on

Sunday morning. Despite my arguments, she thinks that the sermons are more than 25

minutes (over twenty five minutes is important to her especially when soccer was

playing on TV). For one year she has randomly selected 12 Sundays and found the

average time of 24.32 minutes with a standard deviation of 7.17 minutes. Assuming

that the population is normally distributed and using a 0.05 level of significance, is my

daughter correct in thinking that the average length of sermons is more than 25

minutes?

What is the conclusion?

_________________

PAGE 6

17

For a sample of 37 items from a population for which the standard deviation σ = 14, the

sample mean is 340. Construct a 95% confidence interval for the population mean.

(Round your answer(s) to 2 decimal places.)

95% CI = _________ to _________

18

A proponent of private aid to assist those who are suffering from hunger has decided to

take a random sample to estimate the average annual contribution in her community to

world hunger relief. A similar study in a comparable community reported the standard

deviation of giving as $11. Our proponent believes that her estimate, x, should be

within $4 of the true average and with 92-percent confidence. What size sample is

appropriate? (Round your answer(s) to 3 decimal places.)

n = _________

19

A soft drink dispenser is set to automatically dispense drinks and ice in 8 oz. cups. The

machine is set to fill the cups with 7 1/4 oz. so that the liquid will not run over the top of

the cup. The company is getting complaints that the machine is filling the cups too full

and spilling over. When the machine is operating properly, only 1% of the cups will not

be filled properly. The production manager conducted a one-tail hypothesis test at the

0.01 level to check the machine. A sample of 30 fills was measured. What standard

error will be associated with this test? (Round your answer(s) to 4 decimal places.)

_________

PAGE 7

20

Use the data below for regression analysis. (Round your answer(s) to 3 decimal

places.)

x y

108 99

105 98

73 94

90 94

87 105

125 107

y = _______________

R2 = _______________

21

U.S. News and World Report each year conducts a survey of starting salaries in

various career fields. If you were to devise a plan to replicate this study, how large a

sample would you need to take to be 98% certain that your estimate is within $500 of

the true mean starting salary? Assume that σ is $3650. (Round your answer(s) to 3

decimal places.)

n = _________

22

An elementary school teacher learned that 40 percent of school age children have at

least 3 cavities. The teacher has 33 students in his class. What is the standard

deviation? (Round your answer(s) to 2 decimal places.)

Standard deviation = _________

23

A random sample of size 36 is selected from a population whose mean is 455 and

standard deviation is 6. Calculate the probability that the sample mean will lie within 3

units of the true population mean. (Round your answer(s) to 3 decimal places.)

P = _________

PAGE 8

24

For each of the following combinations of n and p, calculate the standard error of the

sampling distribution of the sample proportion p-hat. (Round your answer(s) to 3

decimal places.)

A) n = 100; p = 0.32

σp-hat = _________

B) n = 200; p = 0.64

σp-hat = _________

C) n = 500; p = 0.17

σp-hat = _________

D) n = 1000; p = 0.74

σp-hat = _________

25

Determine the limits of the 95% confidence interval for μ, given that

n = 76; x = 46; and σ = 11.55. (Round your answer(s) to 3 decimal places.)

95% CI = _________ (n1,n2) where n1=lower limit and n2=upper limit

26

In opposing the establishment of a new bank in a community an existing bank stated

that the area to be served by the proposed bank contained 76 percent of its accounts.

An economic consulting firm randomly sampled the households to determine the

sample proportion, p-hat, which had accounts at the existing bank. The sample size

was 225. (Round your answer(s) to 3 decimal places.)

Find the probability that p-hat is: .

A) Less than 69 percent. = _________

B) More than 78 percent. = _________

1

Population assumption: Normal

n = 16; x = 96; s = 13;

H0: μ ≤ 84, H1: μ > 84;

α = 0.01

State the conclusion:

_________________

2

A simple random sample of 10 students is selected from a large college. For the 10

students, the number of days each was absent during the last semester was to be

1, 2, 9, 4, 1, 2, 3, 1, 4, and 4

What is the point estimate for σ, the variance of the number of days absent for the

college’s students? (Round your answer(s) to 3 decimal places.)

σ = _________

3

Population assumption: None

n = 40

x = 5

σ = 3.04

H0: μ ≤ 6.5

H1: μ > 6.5

α = 0.025. (Round your answer(s) to 3 decimal places.)

z = ______

State the conclusion:

_________________

4

The output from a process is normally distributed with a known standard deviation, but

the mean is unknown. 22 different simple random samples, each with n = 9, are to be

drawn from the process, and a 95% confidence interval for the mean is to be

constructed for each sample. What is the probability that at least 19 of the confidence

intervals will actually contain the population mean? Round your answer to the nearest

percent.

________ %

PAGE 2

5

A large bank in a metropolitan area has a large number of secured loans on apartment

facilities throughout the area. Local economic indicators suggest the percentage of

vacant apartments ranges from 6% to 11%. Concerned about the borrowers’ ability to

meet loan obligations on time the bank decides to sample from the apartments used to

secure loans. The officer responsible for the sample decides to allow a maximum error

of the estimate of 0.01 with 99 percent confidence. The officer wishes to take a sample

large enough to cover all proportions within the estimated vacancy range. Compute the

sample size needed for this study. (Round your answer(s) to 3 decimal places.)

_________

6

Use the information given to find the lower and upper critical values for the sample

mean:n = 973

σ = 43.53

μ = 447.3

α = 0.10 (Round your answer(s) to 3 decimal places.)

Lower value = _________

Upper value = _________

7

n = 400;

p-hat = 0.060;

H0: p ≥ 0.05,

H1: p < 0.05;

α = 0.01

Compute the test statistic. (Round your answer(s) to 3 decimal places.)

Appropriate test: _________________

Test statistic = _________

PAGE 3

8

Determine the p-value associated with each of the following values of the standardized

test statistic z. (Round your answer(s) to 3 decimal places.)

A) Two-tail test, with z = 1.5

p-value = _________

B) One-tail test, with z = 1.05

p-value = _________

C) One-tail test, with z = -1.15

p-value = _________

9

An airline, in response to passenger concern, conducts realistic tests to determine the

time needed to evacuate a Boeing 737. Average evacuation time in the past has been

100 seconds with a standard deviation of 15 seconds. The FFA requires tests that

show a planeload of passengers can be evacuated in 97 seconds. If the airline

conducts a sample of 30 tests, what is the probability that the average evacuation time

will be 97 seconds or less? (Round your answer(s) to 3 decimal places.)

P(x-bar ≤ 97) = _________

10

Find the chi-square value for each of the right-tail areas below, given that the degrees

of freedom are 8: (Round your answer(s) to 3 decimal places.)

A) 0.95, Χ2 = _________

B) 0.01 Χ2 = _________

C) 0.025 Χ2 = _________

D) 0.05 Χ2 = _________

PAGE 4

11

The owner of a video store is interested in whether or not there is a difference in the

proportions of VCR movies rented by members and non-members among movie titles.

Three movies are selected and each person who rents them is identified as a member

or non-member. A total of 350 people rent these movies and the responses are:

(Round your answer(s) to 3 decimal places.)

Cross Classification Table:

-------------------------------------------------------------------------------------

[ Movie ]

-------------------------------------------------------------------------------------

| Membership | Witness | Rambo | Karate Kid | Total |

-------------------------------------------------------------------------------------

| Member | 16 | 17 | 72 | 105 |

-------------------------------------------------------------------------------------

| Non-member | 84 | 83 | 78 | 245 |

-------------------------------------------------------------------------------------

| Total | 100 | 100 | 150 | 350 |

-------------------------------------------------------------------------------------

If Table gets all weird: cross classification table by rows:

Table Name: Movie

Row 1: Membership, with 4-Columns: Witness, Rambo, Karate Kid, Total

Row 2: Member, 16, 17, 72, 105

Row 3: Non-member, 84, 83, 78, 245

Row 4: Total, 100, 100, 150, 350

Answer the following:

a. What are the degrees of freedom for the test of equal proportions?

______

b. What is the expected frequency of the cell Rambo and Non-member?

_______________

c. What is the computed value of the test statistic?

Χ2 = _______________

d. What is the critical value for a 0.01 significance level?

_______________

e. What is the conclusion?

_________________

12

Cement for building a dam is delivered by truck. The dispatcher wants to estimate the

average driver time required to load, drive to the dam, unload, and drive back to the

plant. The time is assumed to be normally distributed. Total time required is recorded

for a random sample of 18 with a mean of 546.56 and a standard deviation of 85.53.

Use these data to obtain an 80-percent confidence interval for the average driver time.

(Round your answer(s) to 3 decimal places.)

80% CI = _________ to _________

PAGE 5

13

Raising in-state and out-of-state tuition is supposed to reduce the number of students

in state supported universities. The registrar of a university wants to estimate the

proportion, π, of students who are paying out-of-state tuition on the installment plan (to

later be compared with in-state installment plan payers). A random sample of 90

students who live out-of-state is taken and 39 of them pay tuition on the installment

plan. Find a 99-percent confidence interval for π based on these data. (Round your

answer(s) to 3 decimal places.)

99% CI = _________ to _________

14

A population consisted of 700 cases involving shoplifters. If a random sample of 250

was taken and in 75 cases the offender was under age 18, in how many of the 700

cases would you say the person involved was under age 18? (Round your answer(s) to

3 decimal places.)

Shoplifters (under 18) = _________ cases

(round your answer up to the nearest integer).

15

Determine the limits of the 85% confidence interval for p, given that n = 70; and p-hat =

0.35. (Round your answer(s) to 3 decimal places.)

85% CI = _________ to _________

16

My daughter and I have argued about the average length of our preacher’s sermons on

Sunday morning. Despite my arguments, she thinks that the sermons are more than 25

minutes (over twenty five minutes is important to her especially when soccer was

playing on TV). For one year she has randomly selected 12 Sundays and found the

average time of 24.32 minutes with a standard deviation of 7.17 minutes. Assuming

that the population is normally distributed and using a 0.05 level of significance, is my

daughter correct in thinking that the average length of sermons is more than 25

minutes?

What is the conclusion?

_________________

PAGE 6

17

For a sample of 37 items from a population for which the standard deviation σ = 14, the

sample mean is 340. Construct a 95% confidence interval for the population mean.

(Round your answer(s) to 2 decimal places.)

95% CI = _________ to _________

18

A proponent of private aid to assist those who are suffering from hunger has decided to

take a random sample to estimate the average annual contribution in her community to

world hunger relief. A similar study in a comparable community reported the standard

deviation of giving as $11. Our proponent believes that her estimate, x, should be

within $4 of the true average and with 92-percent confidence. What size sample is

appropriate? (Round your answer(s) to 3 decimal places.)

n = _________

19

A soft drink dispenser is set to automatically dispense drinks and ice in 8 oz. cups. The

machine is set to fill the cups with 7 1/4 oz. so that the liquid will not run over the top of

the cup. The company is getting complaints that the machine is filling the cups too full

and spilling over. When the machine is operating properly, only 1% of the cups will not

be filled properly. The production manager conducted a one-tail hypothesis test at the

0.01 level to check the machine. A sample of 30 fills was measured. What standard

error will be associated with this test? (Round your answer(s) to 4 decimal places.)

_________

PAGE 7

20

Use the data below for regression analysis. (Round your answer(s) to 3 decimal

places.)

x y

108 99

105 98

73 94

90 94

87 105

125 107

y = _______________

R2 = _______________

21

U.S. News and World Report each year conducts a survey of starting salaries in

various career fields. If you were to devise a plan to replicate this study, how large a

sample would you need to take to be 98% certain that your estimate is within $500 of

the true mean starting salary? Assume that σ is $3650. (Round your answer(s) to 3

decimal places.)

n = _________

22

An elementary school teacher learned that 40 percent of school age children have at

least 3 cavities. The teacher has 33 students in his class. What is the standard

deviation? (Round your answer(s) to 2 decimal places.)

Standard deviation = _________

23

A random sample of size 36 is selected from a population whose mean is 455 and

standard deviation is 6. Calculate the probability that the sample mean will lie within 3

units of the true population mean. (Round your answer(s) to 3 decimal places.)

P = _________

PAGE 8

24

For each of the following combinations of n and p, calculate the standard error of the

sampling distribution of the sample proportion p-hat. (Round your answer(s) to 3

decimal places.)

A) n = 100; p = 0.32

σp-hat = _________

B) n = 200; p = 0.64

σp-hat = _________

C) n = 500; p = 0.17

σp-hat = _________

D) n = 1000; p = 0.74

σp-hat = _________

25

Determine the limits of the 95% confidence interval for μ, given that

n = 76; x = 46; and σ = 11.55. (Round your answer(s) to 3 decimal places.)

95% CI = _________ (n1,n2) where n1=lower limit and n2=upper limit

26

In opposing the establishment of a new bank in a community an existing bank stated

that the area to be served by the proposed bank contained 76 percent of its accounts.

An economic consulting firm randomly sampled the households to determine the

sample proportion, p-hat, which had accounts at the existing bank. The sample size

was 225. (Round your answer(s) to 3 decimal places.)

Find the probability that p-hat is: .

A) Less than 69 percent. = _________

B) More than 78 percent. = _________

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