Question

An insurance agent says the standard deviation of the total hospital charges for patients involved in a crash in which the vehicle struck a construction barricade is less than

​$3900.

A random sample of

28

total hospital charges for patients involved in this type of crash has a standard deviation of

​$4700.

At

α=0.10

can you support the​ agent's claim? Use the​ P-value method to test the claim.Identify the null and alternative hypotheses. Let

σ

be the population standard deviation.

A.

H0​:

σ>​$3900

Ha​:

σ≤​$3900

B.

H0​:

σ≤​$3900

Ha​:

σ>​$3900

C.

H0​:

σ≥​$3900

Ha​:

σ<​$3900

D.

H0​:

σ<​$3900

Ha​:

σ≥​$3900

Identify the test statistic.

nothing

​(Round to two decimal places as​ needed.)

Identify the​ P-value.

nothing

​(Round to three decimal places as​ needed.)

Choose the correct conclusion below.

A.

Fail to reject

H0.

There

is

enough evidence at the

10​%

level of significance to support the insurance​ agent's claim.

B.

Fail to reject

H0.

There

is not

enough evidence at the

10​%

level of significance to support the insurance​ agent's claim.

C.

Reject

H0.

There

is not

enough evidence at the

10​%

level of significance to support the insurance​ agent's claim.

D.

Reject

H0.

There

is

enough evidence at the

10​%

level of significance to support the insurance​ agent's claim.4

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: σ >= 3900
Alternative Hypothesis, Ha: σ < 3900

Test statistic,
Χ^2 = (n-1)*s^2/σ^2
Χ^2 = (28 - 1)*4700^2/3900^2
Χ^2 = 39.21

P-value Approach
P-value = 0.939

Fail to reject H0.

There is not enough evidence at the 10​% level of significance to support the insurance​ agent's claim