In a poll, 420 of 1050 randomly selected adults aged 18 or older stated that the
ID: 3289825 • Letter: I
Question
In a poll, 420 of 1050 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 (e) below. (a) Obtain a pcint estimate for the proportion of adults aged 18 or older who feel there is too little spending on national defense. Simplily your answer) (b) Verify that the requirements for constructing a confidence interval about p are satisfiecd Are the requirements for constructing a confidence interval about p satisfied? A. Yes, the requirements for constructing a confidence interval are satisfied. O B. No, te requirement that the sample size is no more than 5% of the population is not satisfied. ° C. No, the requirement that the sample be a simple random sample is not satisfied OD. No, the requirement that ps gre than 10 is not satisfied. c) Construct a 99% confidence interval for the proportion of adults aged 18 or older who believe there is too lite spending on national defense The 99% confidence interval is (DD (Round to three decimal places as needed.) (d) Is it possible that more than 45% of adults aged 18 or older believe there is too little spending on national defense? Is it likely? O A. It is not possible. O B. It is possible, but not likely. OC. It is possible and likely.Explanation / Answer
Answer to the question is as follows:
a. p' = x/n = 420/1050 = 2/5 = .4
b. There are two requirements for constructing meaningful confidence intervals about a population proportion:
i) The size of your sample is no more than 5% of the size of population it was drawn from - not satisfied
ii) np(1-p) >=10 - this is satisfied - 420*.4*.6 = 100.8
B is the right option. In such cases where i) is not satisfied we use a correcting facator to calculcate CI
c. A 99% CI is taken out as:
p^ +/- Z*(sigma/sqrt(n))*sqrt( N-n / N-1) = .4 +/- 2.56*(.4*.6/sqrt(420))*(sqrt((1050-420)/(420-1)) = .363 to .437
d. .45 lies outside the .363 to .437 range . So, mathematically there is still a possibility but the event is NOT likely to happen.
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