Question

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.

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.