Question

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A firm uses a bookkeeping system requiring an average of 1 hour per week per account to keep the accounts current.
a. Assume that you are the sales representative for a firm that handles materials for a new bookkeeping system. You wish to gain statistical support for the contention that your product allows accounts to be handled faster on the average than the old system. Let μ denote the average time required by the new system. Set up the appropriate hypotheses.
b. Discuss the practical consequences of making a Type I and a Type II error.

Answer 1

a. Assume that you are the sales representative for a firm that handles materials for a new bookkeeping system. You wish to gain statistical support for the contention that your product allows accounts to be handled faster on the average than the old system. Let μ denote the average time required by the new system. Set up the appropriate hypotheses.
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Ho: old time - new time = 0
Ha: old time - new time > 0 (claim)
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b. Discuss the practical consequences of making a Type I and a Type II error.
Type I Error: You reject Ho when in fact it is true.
It turns out that your claim is false. The new system does not
reduce the time and the customer is disappointed.
You may lose the client's business.
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Type II Error: You fail to reject Ho when in fact it is false.
Your system really is better but your tests do not show it.
You may never get the customer to buy the service even though
it would have helped him if he had bought it. You lose his business