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1. It is claimed that Proactine, a new medicine for acne, is 75 percent effective. It is applied to the affected area of a group of 15 people. Calculate the probability for the following: (Round your answers to 3 decimal places.)

(a) All 15 will show significant improvement

Probability

(b) Fewer than 9 of 15 will show significant improvement

Probability

(c) That 12 or more people will show significant improvement

Probability

2 You plan to conduct a survey to find what proportion of the workforce has two or more jobs. You decide on the 90 percent confidence level and state that the estimated proportion must be within 3 percent of the population proportion. A pilot survey reveals that 7 of the 48 sampled hold two or more jobs.

How many in the workforce should be interviewed to meet your requirements? (Round up your answer to the next whole number.)

Number of persons to be interviewed

3.In a poll to estimate presidential popularity, each person in a random sample of 1,390 voters was asked to agree with one of the following statements:

1. The president is doing a good job.

2. The president is doing a poor job.

3. I have no opinion.

A total of 550 respondents selected the first statement, indicating they thought the president was doing a good job.

(a) Construct a 98 percent confidence interval for the proportion of respondents who feel the president is doing a good job. (Round your answers to 2 decimal places.)

Confidence interval for the proportion is up to.

(b) Based on your interval in requirement 1, is it reasonable to conclude that a majority (half) of the population believes the president is doing a good job?

(Click to select)YesNo

The distribution of the number of school-age children per family in the Whitehall Estates area of Boise, Idaho, is:

3b) Number of children 0 1 2 3 4

Percent of families 30 25 35 5 5

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

(a) Determine the mean and standard deviation of the number of school-age children per family in Whitehall Estates. (Round your answers to 2 decimal places.)

Mean

Standard deviation

(b) A new school is planned in Whitehall Estates. An estimate of the number of school-age children is needed. There are 500 family units. How many children would you estimate?

Children

Some additional information is needed about only the families having children.

(c-1) Convert the preceding distribution to one for families with children. (Round your answers to 5 decimal places.)

Number of

Children (X) Probability

given Children P(X)

1

2

3

4

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

(c-2) What is the mean number of children among families that have children? (Round your answers to 2 decimal places.)

Mean

4.In a sample of 380 residents of Georgetown County 165 reported they believed the county real estate taxes were too high.

Develop a 95 percent confidence interval for the proportion of residents who believe the tax rate is too high. (Round your answers to 3 decimal places.)

Confidence interval for the proportion of residents is up to .

Assuming 75% constitutes majority, can we conclude that the majority of the taxpayers feel that the taxes are too high?

(Click to select)NoYes

5)A random sample of 21 people employed by the Florida state authority established they earned an average wage (including benefits) of $68 per hour. The sample standard deviation was $5.95 per hour.

(a) What is your best estimate of the population mean? (Omit the "$" sign in your response.)

Estimated population mean $

(b) Develop a 98 percent confidence interval for the population mean wage (including benefits) for these employees. (Round your answers to 2 decimal places.)

Confidence interval for the population mean wage is between and .

(c) How large a sample is needed to assess the population mean with an allowable error of $2 at 99 percent confidence? (Round up your answer to the next whole number.)

Sample

(a) All 15 will show significant improvement

Probability

(b) Fewer than 9 of 15 will show significant improvement

Probability

(c) That 12 or more people will show significant improvement

Probability

2 You plan to conduct a survey to find what proportion of the workforce has two or more jobs. You decide on the 90 percent confidence level and state that the estimated proportion must be within 3 percent of the population proportion. A pilot survey reveals that 7 of the 48 sampled hold two or more jobs.

How many in the workforce should be interviewed to meet your requirements? (Round up your answer to the next whole number.)

Number of persons to be interviewed

3.In a poll to estimate presidential popularity, each person in a random sample of 1,390 voters was asked to agree with one of the following statements:

1. The president is doing a good job.

2. The president is doing a poor job.

3. I have no opinion.

A total of 550 respondents selected the first statement, indicating they thought the president was doing a good job.

(a) Construct a 98 percent confidence interval for the proportion of respondents who feel the president is doing a good job. (Round your answers to 2 decimal places.)

Confidence interval for the proportion is up to.

(b) Based on your interval in requirement 1, is it reasonable to conclude that a majority (half) of the population believes the president is doing a good job?

(Click to select)YesNo

The distribution of the number of school-age children per family in the Whitehall Estates area of Boise, Idaho, is:

3b) Number of children 0 1 2 3 4

Percent of families 30 25 35 5 5

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

(a) Determine the mean and standard deviation of the number of school-age children per family in Whitehall Estates. (Round your answers to 2 decimal places.)

Mean

Standard deviation

(b) A new school is planned in Whitehall Estates. An estimate of the number of school-age children is needed. There are 500 family units. How many children would you estimate?

Children

Some additional information is needed about only the families having children.

(c-1) Convert the preceding distribution to one for families with children. (Round your answers to 5 decimal places.)

Number of

Children (X) Probability

given Children P(X)

1

2

3

4

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

(c-2) What is the mean number of children among families that have children? (Round your answers to 2 decimal places.)

Mean

4.In a sample of 380 residents of Georgetown County 165 reported they believed the county real estate taxes were too high.

Develop a 95 percent confidence interval for the proportion of residents who believe the tax rate is too high. (Round your answers to 3 decimal places.)

Confidence interval for the proportion of residents is up to .

Assuming 75% constitutes majority, can we conclude that the majority of the taxpayers feel that the taxes are too high?

(Click to select)NoYes

5)A random sample of 21 people employed by the Florida state authority established they earned an average wage (including benefits) of $68 per hour. The sample standard deviation was $5.95 per hour.

(a) What is your best estimate of the population mean? (Omit the "$" sign in your response.)

Estimated population mean $

(b) Develop a 98 percent confidence interval for the population mean wage (including benefits) for these employees. (Round your answers to 2 decimal places.)

Confidence interval for the population mean wage is between and .

(c) How large a sample is needed to assess the population mean with an allowable error of $2 at 99 percent confidence? (Round up your answer to the next whole number.)

Sample

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