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The Medical Aid Board wanted to find out if the mean time to settle medical claims of members differs between two major medical schemes - the Green-Aid Fund and the Explorer Fund.
Fourteen Green-Aid Fund medical claims received were randomly selected and monitored, and the sample mean time to settlement was 10.8 days. Assume a population standard deviation of 3.2 days for settlement times of Green-Aid Fund claims. For a random sample of 15 Explorer Fund medical claims received, the average time to settlement was 12.4 days. Assume a population standard deviation of 2.3 days for settlement times of Explorer Fund claims. Assume settlement times are normally distributed.
(a) Estimate, with 95% confidence, the actual average settlement time (in days) for claims received by the Explorer Fund only. Interpret the result.
(b) Can the Medical Aid Board conclude that the Green-Aid Fund settles claims sooner, on average, than the Explorer Fund? Formulate the null and alternative hypothesis and test this hypothesis at the 5% significance level. What conclusion can be drawn?
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