Question

The
sample size necessary to estimate the difference between two
population proportions within an error margin E for a confidence
level of 1 - a can be derived from the following expression E = z ^
* sqrt rho iq 1 n 1 + p 2 q 2 n 2 replace n with n (assuming both
samples are the same size) and replace each of, by 0.5 (since their
values are unknown). Then solve for n. n 2 p 1, q 1 p 2 q 2 Use
this approach to find the size of each sample if you want to
estimate the difference between the proportions of men and women
planning to vote in the next presidential election. Suppose you
want 99% confidence that your error is not greater than
0.02.

Answer #1

The margin of error is defined as,

Let the sample sizes are equal. i.e

The formula is reduced to,

Let

and

The margin of error = 0.02

The z critical value is obtained from the standard normal distribution table for significance level = 0.01.

Now,

Use the expression in the accompanying discussion of sample size
to find the size of each sample if you want to estimate the
difference between proportions of men and women who own
smartphones. Assume that you want 99% confidence that your error
is no more than 0.06.
The sample should include ___ men and ___ women.

Impact of Sample Size on Accuracy Compute the standard error for
sample proportions from a population with proportion p = 0.35 for
sample sizes of n = 20, n = 250, and n = 1100.

Find the minimum sample size required to estimate a population
proportion with a margin of error = 0.05 a confidence level of 90%,
and from a prior study, p is estimated to be .25
(a)
203
(b)
329
(c)
247
(d)
396
(e) 289

Calculate the estimate for the standard error of the difference
between two proportions for each of the following cases. Consider
that the standard error is to be used in confidence interval
calculation. (Give your answers correct to four decimal places.)
The proper TI-84 program to use for these calculations is
PRGM - STDERROR -1 PROPORTION
PRGM - STDERROR -2 MEANS
PRGM - STDERROR -2 PROP-HYP TST
PRGM - STDERROR -2 PROP-CNF INT
(a) n1 = 30, p1' = 0.8, n2...

Use the given data to find the sample size required to estimate
the population proportion. Margin of error: 0.012; confidence
level: 98%; p and q unknown

Determine the sample size needed to obtain an estimate of µ if
the margin of error E = 0.06, σ = 0.75, and the confidence level is
99%
a) Find α for 99% confidence
level.
α =
(b) Find 1 − α/2.
1 − α/2 =
(c) Find zα/2 for a
99% confidence level.
zα/2 =

Find the sample size needed to estimate the percentage of
Independents (also referred to as “swing voters”) among the
registered voters in Illinois. Since these votes could be crucial
to winning the election, we want the error to be no more than 3% at
a 95% confidence level. Assume p and q are unknown.

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.

Estimate the minimum sample size needed to achieve the margin of
error E= 0.023 for a 95% confidence interval

(1 point) (a) Find the size of each of two samples (assume that
they are of equal size) needed to estimate the difference between
the proportions of boys and girls under 10 years old who are afraid
of spiders. Assume the "worst case" scenario for the value of both
sample proportions. We want a 99 99 % confidence level and for the
error to be smaller than 0.02. 0.02. Answer:
(b) Again find the sample size required, as in part...

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