An insurance company is considering settling small claims by mail rather than by

Question

An insurance company is considering settling small claims by mail rather than by the personal attention of agents, hoping thereby to reduce the time of settling such claims. Under the old system claims were settled with a mean time of 33.2 days. The company decides that the new system is worth adopting if it will reduce the mean time to less than 30 days. The company obtains a random sample of 900 small claims by the new system and finds that for this sample X¯ = 29.4 days and s = 8.2 days. Should the company adopt a new plan?

Q. Formulate this as a hypothesis testing problem: state the null and an alternative hypothesis.

Explanation / Answer

Here company wants to claim that mean time to settle the claim by mail is less than 30

so H0:mu=30 vs H1:mu<30

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