Question

A company has devised a new toner cartridge for its laser jet home/office printer that it believes has a longer lifetime (on average) than the one currently being produced. To investigate its length of life, 225 of the new cartridges were tested by counting the number of high-quality printed pages each was able to produce. The sample mean and standard deviation were determined to be 1,511.4 pages and 35.7 pages, respectively. The historical average lifetime for cartridges produced by the current process is 1,502.5 pages; the historical standard deviation is 97.3 pages.

a. What are the appropriate null and alternative hypotheses to test whether the mean lifetime of the new cartridges exceeds that of the old cartridges?

b. Use α = 0.05 to conduct the test in part a. Do the new cartridges have an average lifetime that is statistically significantly longer than the cartridges currently in production?

c. Does the difference in average lifetimes appear to be of practical significance from the perspective of the consumer? Explain.

d. Should the apparent decrease in the standard deviation in lifetimes associated

Answer #1

a:

Hypotheses are:

b;

Here we have

The test statistics is

The p-value is

p-value = P(z > 1.37) = 0.0853

Since p-value is greater than 0.05 so we fail to reject the null hypothesis.

That is, the new cartridges have an average lifetime that is statistically significantly longer than the cartridges currently in production.

c)

The difference in average lifetimes is 1,511.4 - 1,502.5 = 8.9

This difference is small so the difference in average lifetimes does not appear to be of practical significance from the perspective of the consumer.

d)

Hypotheses are;

Test statistics is

Degree of freedom is df=n-1=224

The p-value is: 0.0000

Excel function used for p-value is: "=1-CHIDIST(30.15,224)"

Since p-value is less than 0.05 so we reject the null hypothesis. That is we can conclude that standard deviation decreases.

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