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

question 71

Essay

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?

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Definitions:

Electronic Fund Transfer

A digital transaction that moves funds from one account to another without the use of cash or paper checks.

Overdraft

An overdraft occurs when money is withdrawn from a bank account and the available balance goes below zero, leading to a negative balance.

Dishonored Check

A check that a bank refuses to pay or clear, typically because there are insufficient funds in the account on which it is drawn.

Certified Check

A personal check guaranteed by the issuing bank, ensuring that the check writer has sufficient funds for the check to clear.