P Value Mean Example (σ known)
An insurance company is reviewing its current policy rates. When originally setting the rates they believed
that the average claim amount was $1,800. They are concerned that the true mean is actually higher than
this, because they could potentially lose a lot of money. They randomly select 40 claims, and calculate a
sample mean of $1,950. Assuming that the standard deviation of all claims is $500, and set α = .05, test to
see if the insurance company should be concerned.
Traditional Method First:
Info: n = 40, x = 1950
Claim: µ > $1800, so H0: µ = 1800 & H1: µ > 1800
∝ = 0.05
Critical z-value: 1.645
€
σ = 500
Zc =1.645 x − µ 1950 −1800
=
= 1.90 , the test
σ
500
40
n
statistic falls in the critical region so we reject H0.
Test Statistic: z =
€
P-Value Method:
Press
STAT 1 Input: Stats
µ > 1800
µo: 1800
z = 1.897366596 (test stat)
p = 0.0288897188
σ: 500
x :1950
n: 40
x :1950
n = 40
µ: > µo
€
Calculate
€
Since p < ∝, we reject Ho.
Conclusion: The sample data support the claim that the average claim is higher than
$1800.