A consumer group wants to know if an automobile insurance company with thousands of customers has an average insurance payout for all their customers that is greater than $500 per insurance claim. They know that most customers have zero payouts and a few have substantial payouts. The consumer group collects a random sample of 18 customers and computes a mean payout per claim of $579.80 with a standard deviation of $751.30. Is it appropriate for the consumer group to perform a hypothesis test for the mean payout of all customers

It isn't appropriate for the consumer group to perform a hypothesis test for the mean payout of all customers.

The major reason is because the sample is short and it is given that most consumer has zero payouts.

The size of the sample taken is not enough large. When sample isn't large enough, it represents skewed information of the population.

The population itself contains many customers who have zero payouts, thus the population isn't normally distributed for insurance claim.

Because of these reasons, the sample mean won't help in deducing conclusions about population mean.

Thus, it is inappropriate for the consumer group to perform a hypothesis test for the mean payout of all customers.

Learn more about population mean estimation here:

link

It is not appropriate to perform a hypothesis test for the mean payout of all customers, mostly because the sample is really small.

The first thing you can see is the sample size, it seems to be really small for a company with thousands of customers, is really probably that just 18 of them do not represent accurately the whole population.

We also do know that a large proportion of the population has zero payouts, so the population is skewed.

Just because of these two motives, the mean of the sample most likely does not accurately portray the whole population, thus is not appropriate for the consumer group to perform a hypothesis test for the mean payout of all customers.

If you want to know more about samples and populations, you can read:

link

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step-by-step explanation:

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!