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substantial over the life of...

The cost of ink cartridges for inkjet printers can be substantial over the life of a printer. Printer manufacturers publish the number of pages that can be printed from an ink cartridge in an effort to attract customers. A company claims that its black ink cartridge will yield an average 2,365 pages. To test this claim, an independent lab measured the page count of 56 cartridges and found the average page count to be 2,201.2. Assume the standard deviation for this population is 208. Complete parts a and b.

a. Create a 95% confidence interval.

nothing≤x≤nothing

(Round to two decimal places as needed.)

b. Does this sample support the company's claim? Choose the correct answer below.

A.

Yes, because the company's claim is not between the limits of the confidence interval for the average number of pages yielded by a single black cartridge.

B.

No, because the company's claim is not between the limits of the confidence interval for the average number of pages yielded by a single black cartridge.

C.

No, because the company's claim is between the limits of the confidence interval for the average number of pages yielded by a single black cartridge.

D.

Yes, because the company's claim is between the limits of the confidence interval for the average number of pages yielded by a single black cartridge.According to a government agency, 53.2% of mothers in a certain region were breast-feeding their six-month-old babies in 2016. Suppose a health insurance company would like to estimate the proportion of mothers in the region who breast-fed their children at six months in 2018. A random sample of 216 mothers with six-month-old babies was selected, 118 of which were breast-feeding. Complete parts a through c.

a. Construct a 95% confidence interval to estimate the actual proportion of mothers with six-month-old babies that were breast-feeding in 2018.

The confidence interval has a lower limit of nothing and an upper limit of nothing.

(Round to three decimal places as needed.)

b. What is the margin of error for this sample?

The margin of error is nothing.

(Round to three decimal places as needed.)

c. Is there evidence that this proportion has changed since 2016 based on this sample?

This sample

▼

provides

does not provide

evidence that this proportion has changed since 2016, since the

▼

confidence interval does not include the proportion from 2016.

the margin of error is less than the proportion from 2016.

the margin of error is greater than the proportion from 2016.

confidence interval does not include zero.

the margin of error is greater than zero.

the margin of error is less than zero.

confidence interval includes the proportion from 2016.

confidence interval includes zero.A national air traffic control system handled an average of 47,195 flights during 28 randomly selected days in a recent year. The standard deviation for this sample is 6,257 flights per day. Complete parts a through c below.

a. Construct a 99% confidence interval to estimate the average number of flights per day handled by the system.

The 99% confidence interval to estimate the average number of flights per day handled by the system is from a lower limit of nothing to an upper limit of nothing.

(Round to the nearest whole numbers.)

b. Suppose an airline company claimed that the national air traffic control system handles an average of 50,000 flights per day. Do the results from this sample validate the airline company's claim?

A.

Since the 99% confidence interval does not contain 50,000, it cannot be said with 99% confidence that the sample validates the airline company's claim.

B.

Since the 99% confidence interval contains 50,000, it cannot be said with 99% confidence that the sample validates the airline company's claim.

C.

Since the 99% confidence interval contains 50,000, it can be said with 99% confidence that the sample validates the airline company's claim.

D.

Since the 99% confidence interval does not contain 50,000, it can be said with 99% confidence that the sample validates the airline company's claim.

c. What assumptions need to be made about this population?

A.

Since the sample size is not greater than or equal to 30, one needs to assume that the population follows the Student's t-distribution.

B.

Since the sample size is not greater than or equal to 30, one needs to assume that the population follows the normal probability distribution.

C.

Since the sample size is not greater than or equal to 30, one needs to assume that the population distribution is not very skewed to one side.

D.

Since the sample size is not greater than or equal to 30, one needs to assume that the population distribution is skewed to one side.Determine the sample size n needed to construct a 90% confidence interval to estimate the population proportion when p=0.68 and the margin of error equals 8%.

a. Create a 95% confidence interval.

nothing≤x≤nothing

(Round to two decimal places as needed.)

b. Does this sample support the company's claim? Choose the correct answer below.

A.

Yes, because the company's claim is not between the limits of the confidence interval for the average number of pages yielded by a single black cartridge.

B.

No, because the company's claim is not between the limits of the confidence interval for the average number of pages yielded by a single black cartridge.

C.

No, because the company's claim is between the limits of the confidence interval for the average number of pages yielded by a single black cartridge.

D.

Yes, because the company's claim is between the limits of the confidence interval for the average number of pages yielded by a single black cartridge.According to a government agency, 53.2% of mothers in a certain region were breast-feeding their six-month-old babies in 2016. Suppose a health insurance company would like to estimate the proportion of mothers in the region who breast-fed their children at six months in 2018. A random sample of 216 mothers with six-month-old babies was selected, 118 of which were breast-feeding. Complete parts a through c.

a. Construct a 95% confidence interval to estimate the actual proportion of mothers with six-month-old babies that were breast-feeding in 2018.

The confidence interval has a lower limit of nothing and an upper limit of nothing.

(Round to three decimal places as needed.)

b. What is the margin of error for this sample?

The margin of error is nothing.

(Round to three decimal places as needed.)

c. Is there evidence that this proportion has changed since 2016 based on this sample?

This sample

▼

provides

does not provide

evidence that this proportion has changed since 2016, since the

▼

confidence interval does not include the proportion from 2016.

the margin of error is less than the proportion from 2016.

the margin of error is greater than the proportion from 2016.

confidence interval does not include zero.

the margin of error is greater than zero.

the margin of error is less than zero.

confidence interval includes the proportion from 2016.

confidence interval includes zero.A national air traffic control system handled an average of 47,195 flights during 28 randomly selected days in a recent year. The standard deviation for this sample is 6,257 flights per day. Complete parts a through c below.

a. Construct a 99% confidence interval to estimate the average number of flights per day handled by the system.

The 99% confidence interval to estimate the average number of flights per day handled by the system is from a lower limit of nothing to an upper limit of nothing.

(Round to the nearest whole numbers.)

b. Suppose an airline company claimed that the national air traffic control system handles an average of 50,000 flights per day. Do the results from this sample validate the airline company's claim?

A.

Since the 99% confidence interval does not contain 50,000, it cannot be said with 99% confidence that the sample validates the airline company's claim.

B.

Since the 99% confidence interval contains 50,000, it cannot be said with 99% confidence that the sample validates the airline company's claim.

C.

Since the 99% confidence interval contains 50,000, it can be said with 99% confidence that the sample validates the airline company's claim.

D.

Since the 99% confidence interval does not contain 50,000, it can be said with 99% confidence that the sample validates the airline company's claim.

c. What assumptions need to be made about this population?

A.

Since the sample size is not greater than or equal to 30, one needs to assume that the population follows the Student's t-distribution.

B.

Since the sample size is not greater than or equal to 30, one needs to assume that the population follows the normal probability distribution.

C.

Since the sample size is not greater than or equal to 30, one needs to assume that the population distribution is not very skewed to one side.

D.

Since the sample size is not greater than or equal to 30, one needs to assume that the population distribution is skewed to one side.Determine the sample size n needed to construct a 90% confidence interval to estimate the population proportion when p=0.68 and the margin of error equals 8%.

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