An industrial firm making small battery-powered toys periodically purchases a large number of batteries for use in the toys. To protect itself, the company, by default, believes a new vendor is no good. The policy of the company is never to buy from a vendor unless it has enough evidence at the 0.0075 significance level to indicate that the batteries have a true mean life larger than 70 hours. Historically, the standard deviation of the batteries' life is 3 hours.
A decision is made using evidence from a random sample of 100 batteries from the vendor.
[(a)] What are the appropriate Ho and Ha for this situation?
[(b)] What are the consequences of a Type I Error in the context of this situation?
[(c)] What are the consequences of a Type II Error in the context of this situation?
[(d)] Should the company buy from a vendor if the random sample of 100 batteries from the vendor results in a sample mean life, ybar, = 70.9 hours?
[(e)] Suppose 100 batteries are randomly selected from a vendor, what is the minimum sample mean life, ybar, at which the company decides to buy?