n=60 (sample size)
sigma (population SD) = 800
Rejecttion rule :
Compute z = (xbar-1400) / [800 / sqrt(60)]
xbar = mean of the sample of 60 observations .
If z > 1.64 (critical value that corresponds to 5 % level of significance for a one-tailed test), reject H0, and conclude H1.

b) Type II error : Not rejecting the hypothesis when it’s false.
That is, concluding that avergae claim fell below $1,400 when it exceeded $1,400.

c)

Sample mean 1542
Standard deviation = 800
Standard error of mean = sigma / sqrt(n)
SE = 800/7.746
Standard error of mean 103.2796
z = (xbar-mu) /se
z = (1542-1400) / 103.2796
z = 1.3749
The computed z doesn’t exceed the critical z of 1.64 at the 5 % level.
Do not reject the nul hypotheisis. The claim didn’t exceed $1,400. Base rate need not be raised.

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