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A company that produces pens advertises that a particular model of pen has an average writing lifetime, under controlled conditions (involving the use of a writing machine) of 12 hours. Suppose the mean of a simple random sample of 30 such pens is 11.75 hours. Does this provide statistically significant enough evidence to say that the mean writing lifetime of all such pens falls short of what the company advertises? Assume that it is known that the writing lifetime of all such pens varies according to a Normal distribution with σ = 0.5 hours.
a. State the null hypothesis and the alternative hypotheses for this situation. Also explain in words what each hypothesis is claiming.
b. Conduct the statistical significance test for this problem and explain what conclusion the sample evidence suggests.
c. Identify the p-value from part b. that you computed and explain in general what a p-value measures.
d. Are the results of part b significant at an =0.01 level of significance?
e. Estimate the mean writing lifetime of these pens using a 90% confidence interval.
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