Question

A certain pen has been designed so that true mean writing lifetime under controlled conditions (involving the use of a writing machine) is at least 10 hours. A random sample of 18 pens is selected, the writing lifetime of each is determined, and a normal quantile plot of the resulting data supports the use of a one-sample t test.

For all hypothesis test questions follow the following procedure (1-4) :

1. State the null and alternative hypotheses and your significance level (α)

2. Choose a test statistic and check any requirements or assumptions of that statistic

3. Calculate the observed value of the test statistic and your p-value

4. Write down your decision and interpret it in the context of the original question

(a) What hypotheses should be tested if the investigators believe a priori that the design specification has been satisfied?

(b) What conclusion is appropriate if the hypotheses of part (a) are tested, t = - 2.3, and α = .05?

(c) What conclusion is appropriate if the hypotheses of part (a) are tested, t = - 1.8, and α = .01?

(d) What should be concluded if the hypotheses of part (a) are tested and t = - 3.6?

Answer 1