The accounting at GIECO notices that the average claim might be larger than $180

Question

The accounting at GIECO notices that the average claim might be larger than $1800, which was previously set as a true average claim amount.

2. 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 = 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

Explanation / Answer

Given that,
population mean(u)=1800
standard deviation, =40
sample mean, x =1920
number (n)=45
null, Ho: =1800
alternate, H1: >1800
level of significance, = 0.05
from standard normal table,right tailed z /2 =1.645
since our test is right-tailed
reject Ho, if zo > 1.645
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 1920-1800/(40/sqrt(45)
zo = 20.12
| zo | = 20.12
critical value
the value of |z | at los 5% is 1.645
we got |zo| =20.12 & | z | = 1.645
make decision
hence value of | zo | > | z | and here we reject Ho
p-value : right tail - ha : ( p > 20.12 ) = 0
hence value of p0.05 > 0, here we reject Ho
ANSWERS
---------------
null, Ho: =1800
alternate, H1: >1800
test statistic: 20.12
critical value: 1.645
decision: reject Ho
p-value: 0

have evidence that average claim is larger than 1800

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