Solution to Medical aid board wants to find if the mean time to settle medical claims of … - Sikademy
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Archangel Macsika

Medical aid board wants to find if the mean time to settle medical claims of members differs between 2 major medical schemes. The sample mean time to settlement was 10.8 days. Population standard deviation of 3.2 days for 1 and the other 12.4 days with population deviation 2.3 days Formulate the null and alternative hypothesis and test this hypothesis at the 1% significance level and draw a conclusion?

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The following null and alternative hypotheses need to be tested:



This corresponds to a two-tailed test, and a z-test for two means, with known population standard deviations will be used.

Based on the information provided, the significance level is \alpha = 0.01, and the critical value for a two-tailed test is z_c=2.5758.

The rejection region for this two-tailed test is R = \{z: |z| > 2.5758\}.

The z-statistic is computed as follows:



Since it is observed that |z| = 1.5367 \le 2.5758=z_c , it is then concluded that the null hypothesis is not rejected.

Using the P-value approach:

The p-value is p=2P(Z<-1.5367)=0.124369, and since p = 0.124369 \ge 0.01=\alpha, it is concluded that the null hypothesis is not rejected.

Therefore, there is not enough evidence to claim that the population mean \mu_1 is different than \mu_2, at the \alpha = 0.01 significance level.

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Question ID: mtid-4-stid-46-sqid-1676-qpid-146