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 492 pages. To test this​ claim, an independent lab measured the page count of 42 cartridges and found the average page count to be 487.7. Assume the standard deviation for this population is 44. 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. Yes​, because the​ company's claim is between the lower limit of BLANK pages and the upper limit of BLANK pages for the average number of pages yielded by a single black cartridge.

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

Answer 1

Given that, sample size (n) = 42, sample mean = 487.7 and

population standard deviation = 44

A company claims that its black ink cartridge will yield 492 pages.

Therefore, the null and alternative hypotheses are,

H0 : μ = 492 (Claim)

Ha : μ ≠ 492

This hypothesis test is a two-tailed test.

A 95% confidence level has significance level of 0.05 and critical value is,

The 95% confidence interval for the population mean is,

The 95% confidence interval is (474.39, 501.01)

Since, population mean = 492 is lies in above interval we fail to reject the null hypothesis.

Therefore, we can conclude that the sample support the company's claim.

Answer : A) Yes​, because the​ company's claim is between the lower limit of 474.39 pages and the upper limit of 501.01 pages for the average number of pages yielded by a single black cartridge