In a poll, 206 of 1030 randomly selected adults aged 18 or older stated that the
ID: 3224246 • Letter: I
Question
In a poll, 206 of 1030 randomly selected adults aged 18 or older stated that they believe there is too little spending on national defense. Use this information to complete parts (a) through (d) below.
(a) Obtain a point estimate for the proportion of adults aged 18 or older who feel there is too little spending on national defense. P hat = (Simplify your answer.)
(b) Verify that the requirements for constructing a confidence interval about p are satisfied. Are the requirements for constructing a confidence interval about p satisfied?
A. Yes, the requirements for constructing a confidence interval are satisfied.
B. No, the requirement that the sample be a simple random sample is not satisfied.
C. No, the requirement that n ModifyingAbove p with caret left parenthesis 1 minus ModifyingAbove p with caret right parenthesisnp1p is greater than 10 is not satisfied.
D. No, the requirement that the sample size is no more than 5% of the population is not satisfied.
(c) Construct a 99% confidence interval for the proportion of adults aged 18 or older who believe there is too little spending on national defense.
The 99% confidence interval is ( , ). (Round to three decimal places as needed.)
(d) Is it possible that more than 25% of adults aged 18 or older believe there is too little spending on national defense? Is it likely?
A. It is possible and likely.
B. It is not possible.
C. It is possible, but not likely.
Explanation / Answer
a ) Point estimate = 206 / 1030 = 0.2
b) A. Yes, the requirements for constructing a confidence interval are satisfied.
c) z value for 99% CI = 2.576
CI = p + / - z * sqrt (p ( 1 - p) / n )
= 0.2 + / -2.576 * sqrt ( 0.2 * 0.8 / 1030)
= (0.168 ,0.232)
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