Question

A company with a fleet of 150 cars found that the emissions systems of

4

out of the

24

they randomly tested failed to meet pollution control guidelines. Is this strong evidence that more than

25 %

of the fleet might be out of​ compliance? Test an appropriate hypothesis and state your conclusion. Be sure the appropriate assumptions and conditions are satisfied before you proceed.

Are the assumptions and the conditions to perform a​ one-proportion z-test​ met?

No

Yes                          

State the null and alternative hypotheses. Choose the correct answer below.

A.

H0​:

pequals=0.250.25

HA​:

pgreater than>0.250.25

B.

H0​:

pequals=0.250.25

HA​:

pless than<0.250.25

C.

H0​:

pequals=0.250.25

HA​:

pnot equals≠0.250.25

D.

The assumptions and conditions are not​ met, so the test cannot proceed.

Determine the​ z-statistic. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

zequals=nothing

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

B.

The assumptions and conditions are not​ met, so the test cannot proceed.

Find the​ P-value. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

​P-valueequals=nothing

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

B.

The assumptions and conditions are not​ met, so the test cannot proceed.

What is your​ conclusion? Choose the correct answer below.

A.This is strong evidence that more than

25 %25%

of the fleet is out of compliance.

B.This is strong evidence that less than

25 %25%

of the fleet is out of compliance.

C.This is strong evidence that about

25 %25%

of the fleet is out of compliance.

D.

The assumptions and conditions are not​ met, so the test cannot proceed.

Answer 1

Given :

P0 = 25% = 0.25

n=24

X = 4

P^ = X/n = 4/24 = 0.1667

We will use the one proportion z-test, since we are interested in testing the claim about one population proportion.

Now check a condition for test are satisfied or not.

Therefore,

n*P0 = 24 * 0.25 = 6 < 10

n*(1-P0) = 24 *(1-0.25) = 18 ≥ 10

No, assumptions and the conditions to perform a one proportion z-test met.

Thus, we note that all conditions are not satisfied and thus we should not proceed with the test.