Question

The Wall Street Journal reports that 33% of taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized deductions on their federal income tax return. The mean amount of deductions for this population of taxpayers was $16,642. Assume the standard deviation is σ = $2,400.

(a) What is the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $200 of the population mean for each of the following sample sizes:

30,

60,

150, and

300? (Round your answers to four decimal places.) sample size n = 30 sample size n = 60 sample size n = 150 sample size n = 300

(b) What is the advantage of a larger sample size when attempting to estimate the population mean?

A larger sample increases the probability that the sample mean will be within a specified distance of the population mean.

A larger sample increases the probability that the sample mean will be a specified distance away from the population mean.

A larger sample has a standard error that is closer to the population standard deviation.

A larger sample lowers the population standard deviation.

Answer #1

(b) A larger sample increases the probability that the sample mean
will be within a specified distance of the population mean.

The Wall Street Journal reported that 33% of taxpayers with
adjusted gross incomes between $30,000 and $60,000 itemized
deductions on their federal income tax return. The mean amount of
deductions for this population of taxpayers was $16,642 . Assume
that the standard deviation is $2,812 . Use z-table.
a. What is the probability that a sample of taxpayers from this
income group who have itemized deductions will show a sample mean
within of the $202 of population mean for each...

The Wall Street Journal reported that 33% of taxpayers with
adjusted gross incomes between $30,000 and $60,000 itemized
deductions on their federal income tax return. The mean amount of
deductions for this population of taxpayers was $16,459 . Assume
that the standard deviation is $2,496 . Use z-table. a. What is the
probability that a sample of taxpayers from this income group who
have itemized deductions will show a sample mean within of the $229
of population mean for each...

For the year 2010, 33% of taxpayers with adjusted gross incomes
between $30,000 and $60,000 itemized deductions on their federal
income tax return.† The mean amount of deductions for this
population of taxpayers was $16,642. Assume the standard deviation
is σ = $2,400.
(a) What is the probability that a sample of taxpayers from this
income group who have itemized deductions will show a sample mean
within $200 of the population mean for each of the following sample
sizes: 20,...

In the EAI sampling problem, the population mean is $51,800 and
the population standard deviation is $5,000. When the sample size
is n = 30, there is a 0.4161 probability of obtaining a sample mean
within +/- $500 of the population mean. Use z-table. What is the
probability that the sample mean is within $500 of the population
mean if a sample of size 60 is used (to 4 decimals)? What is the
probability that the sample mean is within...

In the EAI sampling problem, the population mean is $51,700 and
the population standard deviation is $4000 . When the sample size
is n=30 , there is a .5034 probability of obtaining a sample mean
within + or - 500 of the population mean. Use z-table.
a. What is the probability that the sample mean
is within $500 of the population mean if a sample of size 60 is
used (to 4 decimals)?
b. What is the probability that the...

The population proportion is 0.38. What is the probability that
a sample proportion will be within ±0.04 of the population
proportion for each of the following sample sizes? (Round your
answers to 4 decimal places.)
(a) n = 100
(b) n = 200
(c) n = 500
(d) n = 1,000
(e) What is the advantage of a larger sample size? We can
guarantee p will be within ±0.04 of the population proportion p.
There is a higher probability p...

True or False?
1. σM equals the standard deviation
divided by the square root of the sample size
2. Larger samples more accurately reflect the population than
smaller samples
3. If n = 1, the standard error will equal the standard
deviation of the population
4. If a population is skewed, the distribution of sample means
will never be normal
5. The mean for the distribution of samples means is equal to
the mean of the population
6. As the sample...

A random sample is selected from a population with mean μ = 100
and standard deviation σ = 10.
Determine the mean and standard deviation of the x sampling
distribution for each of the following sample sizes. (Round the
answers to three decimal places.)
(a) n = 8 μ = σ =
(b) n = 14 μ = σ =
(c) n = 34 μ = σ =
(d) n = 55 μ = σ =
(f) n = 110...

In the EAI sampling problem, the population mean is 51900 and
the population standard deviation is 4000. When the sample size is
n=30 , there is a 0.5034 probability of obtaining a sample mean
within +/- 500 of the population mean. Use z-table.
a. What is the probability that the sample mean
is within 500 of the population mean if a sample of size 60 is used
(to 4 decimals)?
b. What is the probability that the sample mean
is...

1. Suppose a random sample of 100 elements is selected
from a non-normally distributed
population with a mean of µ = 30 and a standard deviation of σ =
8.
a. What is the expected value of ?̅?
b. What is the standard error of the mean ??̅?
c. What is the sampling distribution of ?̅? Describe its
properties.
d. If we select a random sample of size n = 100, what is the
probability that ?̅will fall
within ±...

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