Question

You want to construct a 95% confidence interval to estimate an unknown population proportion with a...

You want to construct a 95% confidence interval to estimate an unknown population proportion with a margin of error of ±2%. What is the minimum necessary sample size that you should obtain?

Homework Answers

Answer #1

Solution :

Given that,

= 0.5 ( when estimate is not given than use 0.5)

1 - = 1 - 0.5 = 0.5

margin of error = E =+ / - 2% = 0.02

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

Sample size = n = (Z/2 / E)2 * * (1 - )

= (1.96 /  0.02)2 * 0.5 * 0.5

=2401

Sample size = 2401

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Assume that you want to construct a​ 95% confidence interval estimate of a population mean. Find...
Assume that you want to construct a​ 95% confidence interval estimate of a population mean. Find an estimate of the sample size needed to obtain the specified margin of error for the​ 95% confidence interval. The sample standard deviation is given below. Margin of errors=​$6​, standard deviation=​$22 The required sample size is __
How's the economy? A pollster wants to construct a 95 % confidence interval for the proportion...
How's the economy? A pollster wants to construct a 95 % confidence interval for the proportion of adults who believe that economic conditions are getting better. (a) A poll taken in July 2010 estimates this proportion to be 0.41 . Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.02 ? (b) Estimate the sample size needed if no estimate of p is available. Part 1 of 2 (a)...
Construct a 95​% confidence interval to estimate the population proportion with a sample proportion equal to...
Construct a 95​% confidence interval to estimate the population proportion with a sample proportion equal to 0.60 and a sample size equal to 450. LOADING... Click the icon to view a portion of the Cumulative Probabilities for the Standard Normal Distribution table. A 95​% confidence interval estimates that the population proportion is between a lower limit of nothing and an upper limit of nothing.
You want to construct a confidence interval for the mean number of taste buds in top...
You want to construct a confidence interval for the mean number of taste buds in top chefs. Assume the population standard deviation is 900. (a) Calculate the minimum required sample size if you want a margin of error no greater than 300 at the 95% confidence level.   The minimum sample size is ___ chefs. (b) What will cause the minimum required sample size to increase? increasing the confidence level increasing the acceptable margin of error decreasing the acceptable margin of...
Find the minimum sample size n necessary to estimate a population proportion p with a 95%...
Find the minimum sample size n necessary to estimate a population proportion p with a 95% confidence interval that has a margin of error m = 0.03.
"Call me: A sociologist wants to construct a 95% confidence interval for the proportion of children...
"Call me: A sociologist wants to construct a 95% confidence interval for the proportion of children aged 8–12 living in NewYork who own a cell phone.a. A survey by the National Consumers League estimated the nationwide proportion to be 0.56. Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.02?b. Estimate the sample size needed if no estimate of p is31. Changing jobs: A sociologist sampled 200 people who...
Let's say we want to estimate the population proportion of a population. A simple random sample...
Let's say we want to estimate the population proportion of a population. A simple random sample of size 400 is taken from the population. If the sample proportion is 0.32: 1) what is the point estimate of the population proportion? 2) At the 95% level of confidence, what is the margin of error? 3) Based on 2) what is a confidence interval at the 95% confidence level? 4) What is the margin of error if the level of confidence is...
Find the margin of error for the 95% confidence interval used to estimate the population proportion....
Find the margin of error for the 95% confidence interval used to estimate the population proportion. 12) In clinical test with 2349 subjects. 1232 showed improvement from the treatment Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p 13) n=101,x=73;88 percent
Determine the margin of error for a confidence interval to estimate the population proportion for the...
Determine the margin of error for a confidence interval to estimate the population proportion for the following confidence levels with a sample proportion equal to 0.35 and n= 120 the margin of error for a confidence interval to estimate the population portion for 90% confidence level is the margin of error for a confidence interval to estimate the population portion for 95% confidence level is the margin of error for a confidence interval to estimate the population portion for 97%...
You take a random sample of 500 apples from a shipment and construct a 95% confidence...
You take a random sample of 500 apples from a shipment and construct a 95% confidence interval to estimate the proportion that has any residue of pesticides that have been banned by the FDA. You get a margin of error that is five times larger than you would like. What sample size should you use to obtain the desired margin of error? You should use sample size of ___ apples.