For each problem, select the best response. (a) A newspaper conducted a statewid
ID: 3063969 • Letter: F
Question
For each problem, select the best response.
(a) A newspaper conducted a statewide survey concerning a race for state senator. The newspaper took a random sample of 1200 registered voters and found that 620 would vote for the Republican candidate. Let p represent the proportion of registered voters in the state who would vote for the Republican candidate. How large a sample n would you need to estimate p with a margin of error 0.01 with 95 percent confidence? Use p=.5 as the estimated value of p.
A. 49
B. 9604
C. 1500
D. 4800
(b) A radio talk show host with a large audience is interested in the proportion p of adults in his listening area who think the drinking age should be lowered to 18. He asks, 'Do you think the drinking age should be reduced to 18 in light of the fact that 18 year olds are eligible for military service?' He asks listeners to phone in and vote 'yes' if they agree the drinking age should be lowered to 18, and 'no' if not. Of the 100 people who phoned in, 70 answered 'yes.' Which of the following assumptions for inference about a proportion using a confidence interval are violated?
A. The population consists of two types, which may be viewed as successes and failure.
B. The sample size is large enough so that the count of successes np^ is 15 or more.
C. The sample size is large enough so that the count of failures n(1p^) is 15 or more.
D. The data are an random sample from the population of interest.
(c) A newspaper conducted a statewide survey concerning a race for state senator. The newspaper took a random sample of 1200 registered voters and found that 620 would vote for the Republican candidate. Let p represent the proportion of registered voters in the state who would vote for the Republican candidate. A 90 percent confidence interval for p is:
A. 0.517 ± 0.249
B. 0.517 ± 0.014
C. 0.517 ± 0.024
D. 0.517 ± 0.028
Explanation / Answer
a)
We would be using the below formula to estimate n: -
n=Za/2^2*p*1-p/e^2
n=1.96^2*0.5*0.5/0.01^2
n=9604 (B)
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