Question

Given a sample size of n = 529. Let the variance of the population be σ2 = 10.89. Let the mean of the sample be xbar = 15. Construct a 95% confidence interval for µ, the mean of the population, using this data and the central limit theorem.

Use Summary 5b, Table 1, Column 1

- What is the standard deviation (σ) of the population?
- What is the standard deviation of the mean xbar when the sample
size is n, i.e. what is σ
_{xbar}, in terms of σ and n using the central limit theorem? - Is this a one-sided or two-sided problem?
- What value of z should be used in computing k, the margin of error, where

z = k/σ_{xbar} ?

- What is k?
- Write the 95% confidence interval for µ based on xbar and k,

(xbar – k) < µ < (xbar + k)

- Using the Z-score applet “Area from a value”. Let the Mean =
15, and SD = σ
_{xbar}. Choose “Between (xbar -k) and (xbar + k)” using xbar = 15 and your computed value of k. Hit “Recalculate”. Does the probability approximately equal 0.95? (yes or no). Include a screen shot of your answer.

Answer #1

Given a population with a mean of µ = 100 and a
variance σ2 = 12, assume the central limit
theorem applies when the sample size is n ≥ 25. A random
sample of size n = 52 is obtained. What is the probability
that 98.00 < x < 100.76?

Given a population with a mean of µ = 100 and a variance σ2 =
13, assume the central limit theorem applies when the sample size
is n ≥ 25. A random sample of size n = 28 is obtained. What is the
probability that 98.02 < x⎯⎯ < 99.08?

A random sample is drawn from a population having σ = 15.
a. If the sample size is n = 30 and the sample mean x = 100,
what is the 95% confidence interval estimate of the population mean
µ?
b. If the sample size is n = 120 and the sample mean x = 100,
what is the 95% confidence interval estimate of the population mean
µ?
c. If the sample size is n = 480 and the sample...

Assume a normal population with known variance σ2, a random
sample (n< 30) is selected. Let x¯,s represent the sample mean
and sample deviation.
(1)write down the formula: 98% one-sided confidence interval
with upper bound for the population mean.
(2) show how to derive the confidence interval formula in
(1).

Given a population with a mean of µ = 230 and a standard
deviation σ = 35, assume the central limit theorem applies when the
sample size is n ≥ 25. A random sample of size n = 185 is obtained.
Calculate σx⎯⎯

A sample mean, sample size, population standard deviation,
and confidence level are provided. Use this information to complete
parts (a) through (c) below.
x =2323, n=3434, σ=55, confidence level=95%
a.
Use the one-mean z-interval procedure to find a confidence
interval for the mean of the population from which the sample was
drawn.
The confidence interval is from__ to__
b.Obtain the margin of error by taking half the length of the
confidence interval.
What is the length of the confidence interval?...

Given a population with a mean of μ=105 and a variance of
σ2=36, the central limit theorem applies when the sample size is
n≥25. A random sample of size n=25 is obtained.
a. What are the mean and variance of the sampling distribution
for the sample means?
b. What is the probability that x>107?
c. What is the probability that 104<x<106?
d. What is the probability that x≤105.5?

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.

We have a sample of size n = 36 with mean x with bar on top
space equals 12. If population standard deviation, sigma equals 2,
what is the upper limit of 95% confidence interval (zα/2=1.96) of
population mean µ?

A random sample of size n=55 is obtained from a
population with a standard deviation of σ=17.2, and the
sample mean is computed to be x=78.5.
Compute the 95% confidence interval.
Compute the 90% confidence interval.
SHOW WORK

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