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Student: Jorge Ithier

Date: 12/6/16

Instructor: Alexandra Wrigley

Course: Statistics for Decision Making

(100)

Assignment: Week 6 Homework 40 pts

For the same sample statistics, which level of confidence would produce the widest confidence interval? Explain your

reasoning.

Choose the correct answer below.

90%, because as the level of confidence decreases, decreases.zc

99%, because as the level of confidence increases, decreases.zc

90%, because as the level of confidence decreases, increases.zc

99%, because as the level of confidence increases, increases.zc

Construct the confidence interval for the population mean .

c , , , and n= 0.90 = 5.7x = 0.4 = 45

A % confidence interval for is (Round to two decimal places as needed.)90 ( ).,

Construct the confidence interval for the population mean .

c , , , and n= 0.95 = 16.4x = 8.0 = 75

A % confidence interval for is (Round to one decimal place as needed.)95 ( ).,

Find the minimum sample size n needed to estimate for the given values of c, , and E.

c , , and E= 0.95 = 7.1 = 2

Assume that a preliminary sample has at least 30 members.

n (Round up to the nearest whole number.)=

People were polled on how many books they read the previous year. How many subjects are needed to estimate the

number of books read the previous year within one book with % confidence? Initial survey results indicate that

books.

= 15.3

A confidence level requires subjects. 99%

(Round up to the nearest whole number as needed.)

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A doctor wants to estimate the HDL cholesterol of all 20- to 29-year-old females. How many subjects are needed to

estimate the HDL cholesterol within points with confidence assuming Suppose the doctor would be

content with confidence. How does the decrease in confidence affect the sample size required?

2 99% = 12.5?

90%

A 99% confidence level requires subjects.

(Round up to the nearest whole number as needed.)

A confidence level requires subjects.90%

(Round up to the nearest whole number as needed.)

How does the decrease in confidence affect the sample size required?

A. The lower the confidence level the larger the sample size.

B. The lower the confidence level the smaller the sample size.

C. The sample size is the same for all levels of confidence.

Construct the indicated confidence interval for the population mean using the t-distribution.

c , , s , n= 0.99 x = 14.5 = 4.0 = 6

The % confidence interval using a t-distribution is 99 ( ).,

(Round to one decimal place as needed.)

Construct the indicated confidence interval for the population mean using a t-distribution.

c 0. , , s , n= 90 x = 107 = 10 = 10

The confidence interval is ( ).,

(Round to the nearest tenth as needed.)

In a random sample of people, the mean commute time to work was minutes and the standard deviation was

minutes. Assume the population is normally distributed and use a t-distribution to construct a % confidence interval

for the population mean . What is the margin of error of ? Interpret the results.

18 31.2

7.2 90

The confidence interval for the population mean is ( ).,

(Round to one decimal place as needed.)

The margin of error of is .

(Round to one decimal place as needed.)

Interpret the results.

A. If a large sample of people are taken approximately % of them will have commute times

between the bounds of the confidence interval.

B. With % confidence, it can be said that the population mean commute time is between the

bounds of the confidence interval.

C. It can be said that % of people have a commute time between the bounds of the

confidence interval.

D. With % confidence, it can be said that the commute time is between the bounds of the

confidence interval.

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10.

11.

12.

In a survey of adults, say they have started paying bills online in the last year.2962 1435

Construct a 99% confidence interval for the population proportion. Interpret the results.

A 99% confidence interval for the population proportion is .( ),

(Round to three decimal places as needed.)

Interpret your results. Choose the correct answer below.

A. With 99% confidence, it can be said that the sample proportion of adults who say they have

started paying bills online in the last year is between the endpoints of the given confidence

interval.

B. With 99% confidence, it can be said that the population proportion of adults who say they

have started paying bills online in the last year is between the endpoints of the given

confidence interval.

C. The endpoints of the given confidence interval show that adults pay bills online 99% of the

time.

In a survey of women, say they change their nail polish once a week. Construct a confidence interval for

the population proportion of women who change their nail polish once a week.

7000 4431 90%

A % confidence interval for the population proportion is .90 ( ),

(Round to three decimal places as needed.)

A researcher wishes to estimate, with % confidence, the population proportion of adults who are confident with their

country's banking system. His estimate must be accurate within % of the population proportion.

(a) No preliminary estimate is available. Find the minimum sample size needed.

(b) Find the minimum sample size needed, using a prior study that found that % of the respondents said they are

confident with their country's banking system.

(a) What is the minimum sample size needed assuming that no prior information is available?

n (Round up to the nearest whole number as needed.)=

(b) What is the minimum sample size needed using a prior study that found that % of the respondents said they are

confident with their country's banking system?

n (Round up to the nearest whole number as needed.)=

A. Having an estimate of the population proportion has no effect on the minimum sample size

needed.

B. Having an estimate of the population proportion reduces the minimum sample size needed.

C. Having an estimate of the population proportion raises the minimum sample size needed.

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13.

14.

A researcher wishes to estimate, with % confidence, the population proportion of adults who say chocolate is their

favorite ice cream flavor. Her estimate must be accurate within % of the population proportion.

(a) No preliminary estimate is available. Find the minimum sample size needed.

(b) Find the minimum sample size needed, using a prior study that found that % of the respondents said their favorite

flavor of ice cream is chocolate.

(a) What is the minimum sample size needed assuming that no prior information is available?

n (Round up to the nearest whole number as needed.)=

(b) What is the minimum sample size needed using a prior study that found that % of the respondents said their

favorite ice cream flavor is chocolate?

n (Round up to the nearest whole number as needed.)=

A. Having an estimate of the population proportion reduces the minimum sample size needed.

B. Having an estimate of the population proportion raises the minimum sample size needed.

C. Having an estimate of the population proportion has no effect on the minimum sample size

needed.

The table to the right shows the results of a survey in which adults from

Country A, adults from Country B, and adults from Country C were

asked if human activity contributes to global warming. Complete parts (a), (b),

and (c).

2554

1145 1096

Adults who say that human

activity contributes to global

warming

Country A %69

Country B %89

Country C %91

(a) Construct a % confidence interval for the proportion of adults from who say human activity contributes to

global warming.

90 Country A

(Round to three decimal places as needed.)( ),

(b) Construct a % confidence interval for the proportion of adults from who say human activity contributes to

global warming.

90 Country B

(Round to three decimal places as needed.)( ),

global warming.

90 Country C

(Round to three decimal places as needed.)( ),

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15. The table shows the results of a survey in which separate samples of 400

adults each from the East, South, Midwest, and West were asked if traffic

congestion is a serious problem in their community. Complete parts (a) and

(b).

(a) Construct a 95% confidence interval for the proportion of adults from the who say traffic congestion is a serious

problem.

South

The 95% confidence interval for the proportion of adults from the who say traffic congestion is a serious problem is South (

(Round to three decimal places as needed.)

(b) Construct a 95% confidence interval for the proportion of adults from the who say traffic congestion is a serious

problem.

East

The 95% confidence interval for the proportion of adults from the who say traffic congestion is a serious problem is East (

(Round to three decimal places as needed.)

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