The accounting at GEICO notices that the average claim might be larger than $1800, which was previously set as a true average claim amount.
If the actual average is higher, the company will be loosing money in the long run. They ran domly select 45 claims, and calculate a sample mean of S1,920.
Suppose that the variance of claims is known to be equal to S1600.
(a) Set the significance level to α 0.05 and use the hypothesis testing to check if the average claim is larger than $1800.
(b) Find the probability of Type I error.
(c) Find the p-value corresponding to the given sample.
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