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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 2,365pages. 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.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.

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.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.

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