Question

An economist is asked to estimate the average duration of unemployment (measured in months) in a population. From a random sample of 9 spells of unemployment, she finds a sample average duration of 8. Suppose that she knows the population standard deviation of spells is σ = 3.

(a) Find a 90% confidence interval for the population average duration. (b)TestH0 : μ=7againstHA : μ>7withα=0.05.

(c) If the true (but unknown) average duration is in fact μ = 8 then what is the power of the test in part (b)?

Answer #1

According to a study of political prisoners, the mean duration
of imprisonment for 33prisoners with chronic post-traumatic stress
disorder (PTSD) was 33.3 months. Assuming that σ=40months,
determine a 90% confidence interval for the mean duration of
imprisonment, μ, of all political prisoners with chronic PTSD.
Interpret your answer in words.
A 90% confidence interval for the population mean is from ___
months to___months
Interpret the confidence interval. Select the correct choice
below and fill in the answer boxes to complete...

The owner of a factory wants to estimate the mean cost of
manufacturing a product. She takes a random sample of 36 products
and finds the sample mean cost to be $90. Suppose the population
standard deviation is known to be σ = $10.
A) Create a 90% confidence interval for the population mean.
B) Interpret your confidence interval from part (a).
C) Without calculating another confidence interval, if the
sample of 36 products instead had a mean of $200,...

Twelve different video games showing substance use were observed
and the duration times of game play (in seconds) are listed below.
The design of the study justifies the assumption that the sample
can be treated as a simple random sample. Use the data to construct
a 90% confidence interval estimate of μ, the mean duration of
game play
4042
3892
3858
4019
4323
4819
4651
4024
4998
4828
4329
4319
What is the confidence interval estimate of the population mean...

A
95%
confidence interval of
16.6
months to
49.6
months has been found for the mean duration of
imprisonment,
muμ,
of political prisoners of a certain country with chronic
PTSD.
a. Determine the margin of error, E.
b. Explain the meaning of E in this context in terms of the
accuracy of the estimate.
c. Find the sample size required to have a margin of error
of
12
months and a
99%
confidence level. (Use
sigmaσequals=42
months.)d. Find a
99%...

2. A scientist averages several measurements to
estimate the average depth of a river. He wants to be 90% confident
that his estimate is accurate to within 0.4 foot. The population
standard deviation of the depths measured is σ = 4.5 feet.
Find the number of measurements, n, to be included in the
sample.
A 90% confidence requires ___________
measurements.
If the confidence level is changed to 99%, find the number of
measurements, n, to be included in the sample....

An economist would like to estimate the 99% confidence interval
for the average real estate taxes collected by a small town in
California. In a prior analysis, the standard deviation of real
estate taxes was reported as $1,470. [You may find it useful to
reference the z table.] What is the minimum sample size required by
the economist if he wants to restrict the margin of error to
$510

The Queen of Rohan wishes to estimate the mean size of a herd of
horses on the plains. She wished to do so by computing a 98%
confidence interval with a maximum margin of error of 3. She knows,
from past surveys, that the population standard deviation, σ,
tended to be 11.3. What is the minimum sample size necessary to
compute the described confidence interval?

Biologists studying the healing of skin wounds measured the rate
at which new cells closed a cut made in the skin of an anesthetized
newt. Here are data from a random sample of 18 newts, measured in
micrometers (millionths of a meter) per hour: 29, 27, 34, 40, 22,
28, 14, 35, 26, 35, 12, 30, 23, 18, 11, 22, 23, 33.
90% confidence level (22.254,29.080)
(A) Consider a test of H0 : μ = 25 vs. HA : μ...

Question 1
A researcher wishes to find a 90% confidence interval estimate
for an unknown population mean using a sample of size 25. The
population standard deviation is 7.2.
The confidence factor z α 2for this est
Group of answer choices
1.28
1.645
1.96
Question 2
A 90% confidence interval estimate for an unknown population
mean μ is (25.81, 29.51).
The length of this CI estimate is
Group of answer choices
1.96
1.85
3.7
1.645
Question 3
Data below refers...

Determine the sample size necessary under the following
conditions.
a. To estimate μ with σ = 44, E = 3,
and 95% confidence
b. To estimate μ with a range of values from 20
to 88 with E = 2 and 90% confidence
c. To estimate p with p
unknown, E = .04, and 98% confidence
d. To estimate p with E =
.03, 95% confidence, and p thought to be approximately
.70

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