Question

The cost of ink cartridges for inkjet printers can be substantial over the life of a...

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 495 pages. To test this​ claim, an independent lab measured the page count of 55 cartridges and found the average page count to be 486.6. Assume the standard deviation for this population is 45. Using a 95% confidence​interval, does this sample support the​ company's claim? Select the correct choice​ below, and fill in the answer boxes to complete your choice. ​(Round to two decimal places as​needed.)

A. No​, because the​ company's claim is not between the lower limit of ____ pages and the upper limit of ____ pages for the average number of pages yielded by a single black cartridge. B. Yes​, because the​ company's claim is between the lower limit of ____ pages and the upper limit of ____ pages for the average number of pages yielded by a single black cartridge.

Homework Answers

Answer #1

Answer:

Given,

xbar = 486.6

s = 45

n = 55

Here for the 95% confidence interval , z value is 1.96

Now consider,

Interval = (xbar +/- z*s/sqrt(n))

substitute values

= (486.6 +/- 1.96*45/sqrt(55))

= (486.6 +/- 11.8929)

= (486.6 - 11.8929 , 486.6 + 11.8929)

= (474.71 , 498.49)

Here we can say , Yes,the sample support the​ company's claim

i.e.,

495 is included in the CI limits.

So Option B is right answer.

Yes​, because the​ company's claim is between the lower limit of 474.71 pages and the upper limit of 498.49 pages for the average number of pages yielded by a single black cartridge.

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