Question

In: Statistics and Probability

The purchasing manager for a large office complex must decide between two competing brands of fluorescent...

The purchasing manager for a large office complex must decide between two competing brands of fluorescent light bulbs. One is the brand currently used in the building and has a mean life of 900 hours. The new brand is more expensive, but the manufacturer claims that the mean life exceeds that of the current brand.

a. What hypothesis about u, the true mean life for the new brand, should the purchasing manager test? Explain your choice.

b. For the hypothesis of part (a), describe type I and type II errors and consequences.

Solutions

Expert Solution

(a)

H0: Null Hypothesis: 900 ( the mean life does not exceed that of the current brand. )

HA: Alternative Hypothesis: 900 ( the mean life exceeds that of the current brand. )(Claim)

(b)

Type I Error: Rejection of a true null hypothesis.

Suppose in reality, the mean life does not exceed that of the current brand. But, the purchasing manager wrongly concludes that the mean life exceeds that of the current brand. Type I Error is committed in this situation.

The consequence of Type I Error is that the Purchasing manager will procure more expensive new brand wrongly thinking its mean life exceeds that of the current brand., which is not true in reality.

Type II Error: Failure to reject a false null hypothesis.

Suppose in reality, the mean life exceeds that of the current brand. But, the purchasing manager wrongly concludes that the mean life does not exceed that of the current brand. Type II Error is committed in this situation.

The consequence of Type II Error is that the Purchasing manager will not procure more expensive new brand wrongly thinking its mean life does not exceed that of the current brand., which is not true in reality.

orchestra answered 2 years ago
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