Question

According to a Gallup poll about gun ownership, in the year 2016, 270 out of 600 (45%) U.S. households answered “yes” to the question: “Do you have a gun in your home?”.

a. List the requirements for constructing a confidence interval for a proportion and show how the requirements are met for this problem.

b. Construct a 95% confidence interval for the proportion of households who own a gun in the year 2016.

c. Interpret your confidence interval in part “c”. (I am ____% confident that………).

d. Sample Size: A politician wants to know if the proportion of U.S. households who own a gun is on the rise. What size sample should be obtained if the politician wants an estimate within 3 percentage points of the true proportion with 95% confidence if he uses the 2016 estimate of 37.7% (use formula pg. 401)?

Answer 1

(a)

the requirements for constructing a confidence interval for a proportion	how the requirements are met for this problem.
(1) The data must be sampled randomly.	This is not specifically seen as met.
(2) The sample values must be independent of each other.	Since the survey is from U.S. households, this is seen as met.
(3) The sample size should be no more than 10% of population.	Since the population is entire U.S.,, this is seen as met.
(4) The sampling distribution of the statistic is approximately normal.	Since the sample size = n = 600 > 30, Large sample, this is seen as met.

(b)

= 0.05

From Table, critical values of Z = 1.96

Confidence Interval:

So,

Answer is:

(0.41 0.49)

(c)

Interpretation:

I am 95% confident that the confidence interval includes the unknown true population proportion of households who own a gun in the year 2016.

(d)

Sample Size (n) is given by:

Given:

= 0.05

From Table, critical values of Z = 1.96

p = 0.377

e = 0.03

Substituting, we get:

So,

Answer is:

1003