Question

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?

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}
= Z_{0.025} = 1.96

Sample size = n = (Z_{/2}
/ E)^{2} *
* (1 -
)

= (1.96 / 0.02)^{2} * 0.5 * 0.5

=2401

Sample size = 2401

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 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)...

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 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 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.
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 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 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.

1. When constructing a confidence interval to estimate a
population proportion, what affects the size of the margin of
error?
A. The sample size
B. The sample proportion
C. The confidence level
D. All of the above affect the size of the margin of error
E. None of the above affect the size of the margin of error
2. What percentage of couples meet through online dating
apps? A survey of a random sample of couples finds that 12% say...

Construct a 99% confidence interval to estimate the population
proportion with a sample proportion equal to 0.36 and a sample size
equal to 100. A 99% confidence interval estimates that the
population proportion is between a lower limit of ___ and an upper
limit of ___

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 8 minutes ago

asked 16 minutes ago

asked 16 minutes ago

asked 23 minutes ago

asked 27 minutes ago

asked 27 minutes ago

asked 28 minutes ago

asked 45 minutes ago

asked 51 minutes ago

asked 53 minutes ago

asked 56 minutes ago

asked 59 minutes ago