Question

In a recent household telephone survey of 2,870 adults in a certain? country, 28?% reported that they own at least one gun. The researchers want to estimate the true percentage of adults in that country that own at least one gun. Complete parts a through f below.

a. Identify the population of interest to the researchers. Choose the correct answer below.

A.The set of adults that responded to the survey

B.The set of guns in the country

C.The set of adults in the country that own a gun

D.The set of all gun ownership status? (yes/no) values for all adults in the country

b. Identify the parameter of interest to the researchers.

The parameter of interest is ?.

c. Compute an estimate of the population parameter.

?

?(Type an integer or a? decimal.)

d. Form a? 99% confidence interval around the estimate.

(?,?)

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

e. Interpret the confidence interval practically. Choose the correct answer below.

A.One can be? 99% confident the true proportion of gun owners lies at the mean of the above interval.

B.One can be? 99% confident the true proportion of gun owners lies within the above interval.

C.There is a? 99% probability that the true proportion of gun owners is the mean of the interval.

D.One can be? 99% confident the true proportion of gun owners is one of the end points of the above interval.

f. Explain the meaning of the phrase? "99% confident." Choose the correct answer below.

A.It means that? 99% of the possible population proportions will fall into this confidence interval.

B.It means that there is a? 99% probability that the true proportion of gun owners will be in the confidence interval formed from the first sample taken.

C.It means that? 99% of the possible sample proportions will fall into this confidence interval.

D.It means that? 99% of all similarly formed intervals will contain the true proportion of gun owners in the country.

Answer 1

a. population of interest = The set of all gun ownership status? (yes/no) values for all adults in the country

Option D is correct

(b)

Parameter of interest = True proportion of all people who has the status of gun ownership

(c) Population parameter = 0.28

(d) 99% confidence interval = p^ +- Z_99% se_p

= 0.28 +- 2.576 * sqrt (0.28 * 0.72/2870)

= 0.28 +- 0.0216

= (0.26, 0.30)

(e) One can be? 99% confident the true proportion of gun owners lies within the above interval.

(f) Here option b is correcthere.