21. )In a recent poll, 273 people were asked if they liked dogs, and 74% said th
ID: 3238365 • Letter: 2
Question
21.)In a recent poll, 273 people were asked if they liked dogs, and 74% said they did. Find the margin of error of this poll, at the 90% confidence level.
20.)Assume that a sample is used to estimate a population proportion p. Find the margin of error M.E. that corresponds to a sample of size 208 with 25% successes at a confidence level of 99.5%.
M.E. = % Round to 4 places.-------------
24.)Assume that a sample is used to estimate a population proportion p. Find the 99.9% confidence interval for a sample of size 169 with 117 successes. Enter your answer as an open-interval (i.e., parentheses) using decimals (not percents) accurate to three decimal places.
99.9% C.I. = ----------
28.)A political candidate has asked you to conduct a poll to determine what percentage of people support her.
If the candidate only wants a 5% margin of error at a 95% confidence level, what size of sample is needed?
Give your answer in whole people.----------.
29.)
You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p*=60%p*=60%. You would like to be 98% confident that you estimate is within 0.2% of the true population proportion. How large of a sample size is required?
n =
Do not round mid-calculation. However, use a critical value accurate to three decimal places.
30.)
You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion. Your would like to be 99% confident that you estimate is within 5% of the true population proportion. How large of a sample size is required?
n = ---------
Do not round mid-calculation. However, use a critical value accurate to three decimal places.
Explanation / Answer
21.)In a recent poll, 273 people were asked if they liked dogs, and 74% said they did. Find the margin of error of this poll, at the 90% confidence level.
Answer:
For 90% confidence interval critical Z=1.645
Margin of error =1.645*sqrt(0.74*(1-0.74)/273)= 0.0437
20.)Assume that a sample is used to estimate a population proportion p. Find the margin of error M.E. that corresponds to a sample of size 208 with 25% successes at a confidence level of 99.5%.
M.E. = % Round to 4 places.-------------
Answer:
For 99.5% confidence, critical Z=2.807
Margin of error =2.807*sqrt(0.25*(1-0.25)/208) = 0.0843 = 8.43%
24.)Assume that a sample is used to estimate a population proportion p. Find the 99.9% confidence interval for a sample of size 169 with 117 successes. Enter your answer as an open-interval (i.e., parentheses) using decimals (not percents) accurate to three decimal places.
99.9% C.I. = ----------
Answer:
For 99.9% confidence, critical Z=3.291
Margin of error =3.291*sqrt((117/169)*(1-117/169)/169) = 0.117
So 99.9% CI= 117/169-0.117 , 117/169+117/169
=(0.575 0.809)
28.)A political candidate has asked you to conduct a poll to determine what percentage of people support her.
If the candidate only wants a 5% margin of error at a 95% confidence level, what size of sample is needed?
Give your answer in whole people.----------.
Answer:
For 95% confidence, critical Z=1.96 with ME=0.05 and conservative estimate of population proportion p=0.5
So, n>= p*(1-p)*(z/ME)2=0.5*(1-0.5)*(1.96/0.05)2=384.16
So, n=385
29.)
You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p*=60%p*=60%. You would like to be 98% confident that you estimate is within 0.2% of the true population proportion. How large of a sample size is required?
n =
Do not round mid-calculation. However, use a critical value accurate to three decimal places.
Answer:
For 98% confidence, critical Z=2.326 with ME=0.002 and estimate of population proportion p=0.6
So, n>= p*(1-p)*(z/ME)2=0.6*(1-0.6)*(2.326/0.002)2=324616.56
So, n=324617
30.)
You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion. Your would like to be 99% confident that you estimate is within 5% of the true population proportion. How large of a sample size is required?
n = ---------
Do not round mid-calculation. However, use a critical value accurate to three decimal places.
Answer:
For 95% confidence, critical Z=1.96 with ME=0.05 and conservative estimate of population proportion p=0.5
So, n>= p*(1-p)*(z/ME)2=0.5*(1-0.5)*(1.96/0.05)2=384.16
So, n=385
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