Question

Suppose that a random sample of 50 bottles of a particular brand of cough syrup is selected and the alcohol content of each bottle is determined. Let μ denote the average alcohol content for the population of all bottles of the brand under study. Suppose that the resulting 95% confidence interval is (7.6, 9.2). (a) Would a 90% confidence interval calculated from this same sample have been narrower or wider than the given interval? Explain your reasoning. The 90% would be narrower since the z critical value for 90% is larger than the z critical value for 95%. The 90% would be the same since the z critical value for 90% is the same as the z critical value for 95%. The 90% would be narrower since the z critical value for 90% is smaller than the z critical value for 95%. The 90% would be wider since the z critical value for 90% is smaller than the z critical value for 95%. The 90% would be wider since the z critical value for 90% is larger than the z critical value for 95%. (b) Consider the following statement: There is a 95% chance that μ is between 7.6 and 9.2. Is this statement correct? Why or why not? It is a correct statement. Each interval contains the mean by definition. It is not a correct statement. We are 95% confident in the general procedure for creating the interval, but the mean may or may not be enclosed in this interval. It is a correct statement. There is only a 5% chance that the mean is not between these values. It is not a correct statement. Each interval contains the mean by definition. It is not a correct statement. There is a 5% chance that the mean is between these values. (c) Consider the following statement: We can be highly confident that 95% of all bottles of this type of cough syrup have an alcohol content that is between 7.6 and 9.2. Is this statement correct? Why or why not? It is not a correct statement. The interval is an estimate for the sample mean, not a boundary for population values. It is not a correct statement. The interval is an estimate for the sample mean, not a boundary for sample values. It is not a correct statement. The interval is an estimate for the population mean, not a boundary for population values. It is a correct statement. This is the definition of a confidence interval. It is a correct statement. This interval is a great estimate of boundaries for population values. (d) Consider the following statement: If the process of selecting a sample of size 50 and then computing the corresponding 95% interval is repeated 100 times, 95 of the resulting intervals will include μ. Is this statement correct? Why or why not? It is not a correct statement. 90 out of the 100 intervals will contain the mean. It is a correct statement. This is guaranteed by the definition of confidence interval. It is a correct statement. Since we are taking the same sample, we expect all intervals to contain the mean. It is not a correct statement. We expect 5 out of the 100 intervals to contain the mean. It is not a correct statement. We expect 95 out of 100 intervals will contain the mean, but we don't know this to be true.

Answer #1

You are given the sample mean and the sample standard deviation.
Use this information to construct the 90% and 95% confidence
intervals for the population mean. Interpret the results and
compare the widths of the confidence intervals. If convenient, use
technology to construct the confidence intervals. A random sample
of 5050 home theater systems has a mean price of $145.00145.00 and
a standard deviation is $18.7018.70.
The 90% confidence interval is
The 95% confidence interval is
Interpret the results. Choose...

You are given the sample mean and the population standard
deviation. Use this information to construct the 90% and 95%
confidence intervals for the population mean. Interpret the results
and compare the widths of the confidence intervals. If convenient,
use technology to construct the confidence intervals. A random
sample of 55 home theater systems has a mean price of $115.00.
Assume the population standard deviation is $17.70.
1. The 90% confidence interval is?
2. Interpret the results. Choose the correct...

Suppose a random sample of 50 college students is asked if they
regularly eat breakfast. A 95% confidence interval for the
proportion of all students that regularly eat breakfast is found to
be 0.69 to 0.91. If a 90% confidence interval was calculated
instead, how would it differ from the 95% confidence interval?
The 90% confidence interval would be wider.
The 90% confidence interval would be narrower.
The 90% confidence interval would have the same width as the 95%
confidence...

You are given the sample mean and the population standard
deviation. Use this information to construct the 90% and 95%
confidence intervals for the population mean. Interpret the results
and compare the widths of the confidence intervals. If convenient,
use technology to construct the confidence intervals. A random
sample of 45 45 home theater systems has a mean price of $ 137.00
137.00. Assume the population standard deviation is $ 16.60 16.60.
Construct a 90% confidence interval for the population...

You are given the sample mean and the population standard
deviation. Use this information to construct the 90% and 95%
confidence intervals for the population mean. Interpret the results
and compare the widths of the confidence intervals. If convenient,
use technology to construct the confidence intervals.
A random sample of 35 home theater systems has a mean price of
$128.00 Assume the population standard deviation is $19.30
Construct a 90% confidence interval for the population
mean.
The 90% confidence interval...

A researcher measured the body temperatures of a randomly
selected group of adults. He wishes to estimate the average
temperature among the adult population. Summaries of the data he
collected are presented in the table below. Complete parts? (a)
through? (d) below.
Summary
Count
Mean
Median
MidRange
StdDev
Range
IntQRange
tempeture
43
98.457
98.000
98.600
0.8847
2.800
1.050 ?
a) Would a 90?% confidence interval be wider or narrower than
the 98?% confidence? interval? Explain. Choose the correct...

A simple random sample with n=50 provided a sample mean of 22.5
and a sample standard deviation of 4.2 .
a. Develop a 90% confidence interval for the
population mean (to 1 decimal).
( , )
b. Develop a 95% confidence interval for the
population mean (to 1 decimal).
( , )
c. Develop a 99% confidence interval for the
population mean (to 1 decimal).
( , )
d. What happens to the margin of error and the
confidence interval...

he sample data below have been collected based on a simple
random sample from a normally distributed population. Complete
parts a and b.
7
5
0
7
6
5
9
8
9
3
a. Compute a 90% confidence interval estimate for the
population mean. The 90% confidence interval for the population
mean is from ______ to _________ (Round to two decimal places as
needed. Use ascending order.)
b. Show what the impact would be if the confidence level is
increased...

3. A sample of 95 results in 57 successes. Use
Table 1. Please do not post if you are unsure. THANK YOU!
a. Calculate the point estimate for the population proportion of
successes. (Do not round intermediate calculations.
Round your answer to 3 decimal places.)
POINT ESTIMATE
0.600 (CORRECT)
b. Construct 99% and 90% confidence intervals for the population
proportion. (Round intermediate calculations to 4
decimal places. Round "z-value" and final answers to 3 decimal
places.)
Confidence Level
Confidence...

A study based on a random sample of 17 reported a sample mean of
65 with a sample standard deviation of 4.
Calculate a 95% Confidence interval.
What is the margin of error?
If we calculated a 90% confidence interval, as compared to your
answer in part b, would your margin of error increase: (choose
one)
increase
decrease
stay the same
If we increase the sample size to 50 persons, but the reported
sample mean and sample standard deviation stayed...

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