A certain pen has been designed so that "true" average writing lifetime under controlled conditions (involving the use of a writing machine) is at least 12 hours. A random sample of 18 pens is selected, the writing lifetime of each is determined, and a normal probability plot of the resulting data supports the use of a one-sample t test.
a. What hypotheses should be tested if the investigator believe a priori that the design specification has been satisfied?
b. What conclusion is appropriate if the hypotheses of part (a) are tested, t = -2.5, and $\alpha = .05$
?
c. What conclusion is appropriate if the hypotheses of part (a) are tested, t = -2, and $\alpha = .01$
?
d. What should be concluded if the hypotheses of part (a) are tested and t = -3.25?

Question

A certain pen has been designed so that "true" average writing lifetime under controlled conditions (involving the use of a writing machine) is at least 12 hours. A random sample of 18 pens is selected, the writing lifetime of each is determined, and a normal probability plot of the resulting data supports the use of a one-sample t test.
a. What hypotheses should be tested if the investigator believe a priori that the design specification has been satisfied?
b. What conclusion is appropriate if the hypotheses of part (a) are tested, t = -2.5, and $\alpha = .05$ 
? 
c. What conclusion is appropriate if the hypotheses of part (a) are tested, t = -2, and $\alpha = .01$ 
? 
d. What should be concluded if the hypotheses of part (a) are tested and t = -3.25?

Quizplus · Accepted Answer

The Answer of A certain pen has been designed so that "true" average writing lifetime under controlled conditions (involving the use of a writing machine) is at least 12 hours. A random sample of 18 pens is selected, the writing lifetime of each is determined, and a normal probability plot of the resulting data supports the use of a one-sample t test.
a. What hypotheses should be tested if the investigator believe a priori that the design specification has been satisfied?
b. What conclusion is appropriate if the hypotheses of part (a) are tested, t = -2.5, and $\alpha = .05$ 
? 
c. What conclusion is appropriate if the hypotheses of part (a) are tested, t = -2, and $\alpha = .01$ 
? 
d. What should be concluded if the hypotheses of part (a) are tested and t = -3.25?

A Certain Pen Has Been Designed So That "True" Average α=.05\alpha = .05α=.05

A Certain Pen Has Been Designed So That "True" Average $\alpha = .05$