(1 point) For each problem, select the best response (a) A newspaper conducted a
ID: 3311539 • Letter: #
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(1 point) For each problem, select the best response (a) A newspaper conducted a statewide survey concerning the 1998 race for state senator. The newspaper took a SRS 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 the guess p - .5 as the value of p A. 1500 B. 9604 C. 49 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 sample size is large enough so that the count of failures n(1 -p) is 15 or more B. The sample size is large enough so that the count of successes np'is 15 or more C. The population is at least ten times as large as the sample D. The data are an SRS from the population of interest (c) A newspaper conducted a statewide survey concerning the 1998 race for state senator. The newspaper took a SRS 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 ± 0.024 C. 0.517 ± 0.028 D. 0.517 ± 0.014Explanation / Answer
a) here margin of error E =0.01 ; for 95% CI ; z=1.96
therefore required sample size n=p(1-p)*(z/E)2 =9604
option B
b)
here option D is correct
c)
sample proportion phat=620/1200=0.517
std error =(p(1-p)/n)1/2 =0.0144
for 90% CI ; z=1.645
therefore 90% Confidence interval =phat -/+ z*Std error =0.517 +/- 0.024
option B
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