Question

When σ is unknown and the sample is of size n ≥ 30, there are two methods for computing confidence intervals for μ. Method 1: Use the Student's t distribution with d.f. = n − 1. This is the method used in the text. It is widely employed in statistical studies. Also, most statistical software packages use this method. Method 2: When n ≥ 30, use the sample standard deviation s as an estimate for σ, and then use the standard normal distribution. This method is based on the fact that for large samples, s is a fairly good approximation for σ. Also, for large n, the critical values for the Student's t distribution approach those of the standard normal distribution. Consider a random sample of size n = 81 with sample mean x = 45.4 and sample standard deviation s = 4.8. (d) Compute 90%, 95%, and 99% confidence intervals for μ using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal. 90% 95% 99% lower limit upper limit

Answer #1

When σ is unknown and the sample is of size n
≥ 30, there are two methods for computing confidence intervals for
μ.
Method 1: Use the Student's t distribution with
d.f. = n − 1.
This is the method used in the text. It is widely employed in
statistical studies. Also, most statistical software packages use
this method.
Method 2: When n ≥ 30, use the sample standard
deviation s as an estimate for σ, and then use
the...

When ? is unknown and the sample is of size
n?30, there are two methods for computing confidence
intervals for ?.
Method 1: Use the Student's t distribution with
d.f.= n?1.
This is the method used in the text. It is widely employed in
statistical studies. Also, most statistical software packages use
this method.
Method 2: When n ? 30, use the sample standard
deviation sas an estimate for ?, and then use the
standard normal distribution.
This method is...

a.) Given a normal distribution with σ = 0.380. Find the
required sample size for a 95% confidence level (estimating the
mean), given a margin-of-error of 6%.
b.) Given the sample results taken from a normal population
distribution: mean = 4.65, σ = 0.32, and n = 17.
For a 99% confidence interval, find the margin-of-error for the
population mean. (use 2 decimal places)
c.) Given the sample results taken from a normal population
distribution: mean = 1.25, σ =...

Use the sample information x¯ = 34, σ = 4,
n = 10 to calculate the following confidence intervals for
μ assuming the sample is from a normal population.
(a) 90 percent confidence. (Round your
answers to 4 decimal places.)
The 90% confidence interval is from to
(b) 95 percent confidence. (Round your
answers to 4 decimal places.)
The 95% confidence interval is from to
(c) 99 percent confidence. (Round your
answers to 4 decimal places.)
The...

Use the sample information x¯x¯ = 36, σ = 7, n
= 20 to calculate the following confidence intervals for μ
assuming the sample is from a normal population.
(a) 90 percent confidence. (Round your
answers to 4 decimal places.)
The 90% confidence interval is from to
(b) 95 percent confidence. (Round your
answers to 4 decimal places.)
The 95% confidence interval is from to
(c) 99 percent confidence. (Round your
answers to 4 decimal places.)
The 99% confidence...

The Central Limit Theorem says that when sample size n is taken
from any population with mean μ and standard deviation σ when n is
large, which of the following statements are true?
The distribution of the sample mean is approximately
Normal.
The standard deviation is equal to that of the population.
The distribution of the population is exactly Normal.
The distribution is biased.

A simple random sample of size n is drawn from a population that
is normally distributed. The sample mean, x, is found to be 113,
and the sample standard deviation, s, is found to be 10.
(a) Construct a 90% confidence interval about μ if the sample
size, n, is 22.
(b) Construct a 90% confidence interval about μ if the sample
size, n, is 15.
(c) Construct an 80% confidence interval about μ if the
sample size, n, is...

Use the sample information x¯ = 35, σ = 7, n = 16 to calculate
the following confidence intervals for μ assuming the sample is
from a normal population. (a) 90 percent confidence. (Round your
answers to 4 decimal places.) The 90% confidence interval is from
to (b) 95 percent confidence. (Round your answers to 4 decimal
places.) The 95% confidence interval is from to (c) 99 percent
confidence. (Round your answers to 4 decimal places.) The 99%
confidence interval...

(05.02 LC)
The Central Limit Theorem says that when sample size n is taken
from any population with mean μ and standard deviation σ when n is
large, which of the following statements are true? (4 points)
I. The distribution of the sample mean is exactly Normal.
II. The distribution of the sample mean is approximately
Normal.
III. The standard deviation is equal to that of the
population.
IV. The distribution of the population is exactly Normal.
a
I and...

A sample of n = 16 is to be taken from a distribution
that can reasonably be assumed
to be Normal with a standard deviation σ of 100. The sample mean
comes out to be 110.
1. The standard error of the mean, that is, the standard deviation
of the sample mean,
is σx¯ = σ/√
n. What is its numerical value?
2. The 97.5 percentile, 1.96, of the standard Normal distribution
is used for a 95% confi-
dence interval....

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