A proponent of a new proposition on a ballot wants to know the population percentage of people who support the bill. Suppose a poll is​ taken, and 589 out of 1000 randomly selected people support the...





A proponent of a new proposition on a ballot wants to know the population percentage of people who support the bill. Suppose a poll is​ taken, and
589

out of
1000

randomly selected people support the proposition. Should the proponent use a hypothesis test or a confidence interval to answer this​ question? Explain. If it is a hypothesis​ test, state the hypotheses and find the test​ statistic, p-value, and conclusion. Use a
5​%

significance level. If a confidence interval is​ appropriate, find the approximate
90​%

confidence interval. In both​ cases, assume that the necessary conditions have been met.





Should the proponent use a hypothesis test or a confidence​ interval? (If both a hypothesis test and a confidence interval could be​ used, choose the simpler​ one.)






A.


The proponent should use a confidence interval because the proponent wants to know the proportion of the population who will vote for the proposition. A hypothesis test would be impossible.






B.


The proponent should use a confidence interval because the proponent wants to know the proportion of the population who will vote for the proposition.​ However, the proponent could also use a hypothesis test.






C.


The proponent should use a hypothesis test because the proponent wants to know whether or not the proposition will pass. A confidence interval would be useless.






D.


The proponent should use a hypothesis test because the proponent wants to know whether or not the proposition will pass.​ However, the proponent could also use a confidence interval.





Determine the null and alternative hypotheses for the hypothesis test. Let p denote the population proportion of voters in favor of the proposition. Select the correct choice below​ and, if​ necessary, fill in the answer boxes within your choice.

​(Type integers or decimals. Do not​ round.)






A.



H0​:

p=nothing



Ha​:

p<>







B.



H0​:

p<>



Ha​:

p>nothing







C.



H0​:

p>nothing



Ha​:

p<>







D.



H0​:

p=nothing



Ha​:

p≠nothing







E.



H0​:

p=nothing



Ha​:

p>nothing







F.


Hypotheses are not appropriate. The proponent should use a confidence interval.





Find the test statistic for the hypothesis test. Select the correct choice below​ and, if​ necessary, fill in the answer box within your choice.







A.



z=nothing


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






B.


A test statistic is not appropriate. The proponent should use a confidence interval.





Find the​ p-value. Select the correct choice below​ and, if​ necessary, fill in the answer box within your choice.







A.



​p-value=nothing


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






B.


A​ p-value is not appropriate. The proponent should use a confidence interval.





Determine the proper conclusion to the hypothesis test. Choose the correct answer below.







A.



Do not reject

H0.

There
is

enough evidence to conclude that the proposition will pass.






B.



Do not reject

H0.

There
is not

enough evidence to conclude that the proposition will pass.






C.



Reject

H0.

There
is

enough evidence to conclude that the proposition will pass.






D.



Reject

H0.

There
is not

enough evidence to conclude that the proposition will pass.






E.


A test conclusion is not appropriate. The proponent should use a confidence interval.





Construct an approximate
90​%

confidence interval for the population proportion p of voters in favor of the proposition. Select the correct choice below​ and, if​ necessary, fill in the answer boxes within your choice.







A.


,

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






B.


A confidence interval is not appropriate. The proponent should use a hypothesis test.










Click to select and enter your answer(s).

Jun 09, 2022
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