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
492492
pages. To test this​ claim, an independent lab measured the page count of
4949
cartridges and found the average page count to be
486.1486.1.
Assume the standard deviation for this population is
4444.
Using a
9595​%
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.
YesYes​,
because the​ company's claim
isnothing
between the lower limit of
nothing
pages and the upper limit of
nothing
pages for the average number of pages yielded by a single black cartridge.
B.
NoNo​,
because the​ company's claim
isnbsp not not
between the lower limit of
nothing
pages and the upper limit of
nothing
pages for the average number of pages yielded by a single black cartridge.

Answer 1

95% confidence interval for is

- Z * / sqrt(n) < < + Z * / sqrt(n)

486.1 - 1.96 * 44 / sqrt(49) < < 486.1 + 1.96 * 44 / sqrt(49)

473.78 < < 498.42

95% CI is ( 473.78 , 498.42)

Claimed mean 492 is between above confidence interval so we have sufficient evidence to support

the claim.

Yes, because the company's claim is 492 between lower limit of 473.78 and upper limit of 498.42

pages for the average number of pages yielded by a single black cartridge.