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.