Question
In: Math
Suppose that a random sample of 50 bottles of a particular brand of cough syrup is selected
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 (8.0, 9.6).
a. Would a \(90 \%\) confidence interval calculated from this same sample have been narrower or wider than the given interval? Explain your reasoning.
b. Consider the following statement: There is a \(95 \%\) chance that \(\mu\) is between 8 and \(9.6\). Is this statement correct? Why or why not?
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 \(8.0\) and \(9.6\). Is this statement correct? Why or why not?
d. Consider the following statement: If the process of selecting a sample of size 50 and then computing the corresponding 955 interval ire repeated 100 times, 95 of the resulting intervals will include \(\mu\). Is this statement correct? Why or why not?
Solutions
milcah answered 2 years agoRelated Solutions
Suppose that a random sample of 50 bottles of a particular brand of cough syrup is...
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 u denote the average alcohol content for the population of all bottles of the brand under study. Suppose that the resulting 95% confidence interval is (7.1, 9.8). (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 wider...
Suppose that a random sample of 50 bottles of a particular brand of cough syrup is...
Suppose that a random sample of 50 bottles of a particular brand of cough syrup is selectedand the alcohol content of each bottle is determined. Let denote the average alcohol contentfor the population of all bottles of the brand under study. Suppose that the resulting 95%confidence interval is (7.8, 9.4).a) Would a 90% confidence interval calculated from this same sample have been narroweror wider than the given interval? Explain your reasoning.b) Consider the following statement: There is a 95% chance...
A random sample of 50 bottles of a brand of cough syrup is selected, the alcohol...
A random sample of 50 bottles of a brand of cough syrup is selected, the alcohol content of each bottle is calculated Let μ be the average alcohol content for the population of all bottles of the brand under consideration. The resulting 95% confidence interval is (7.8,9.4) (a) Would a 90% confidence interval calculated from the same sample be wider or narrower? Explain. (b) Consider the statement: there is a 95% chance that is between 7.8 and 9.4. Is this correct? Explain. (c)...
Suppose a random sample of 50 bottles of "CoughGone" cough syrup was collected and the alcohol...
Suppose a random sample of 50 bottles of "CoughGone" cough syrup
was collected and the alcohol content (in wt. percent) of each
bottle measured. A 95 % confidence interval for bottle true mean
alcohol content, μ, was then determined from these data to be (6.7,
9.3). It was assumed that the variance of the alcohol distribution
was known.
a.) What is the value of the sample mean, x̄ ?(Give answer to
two places past decimal.)
b.) What is the value...
You randomly select and measure the contents of 10 bottles of cough syrup. The results (in...
You randomly select and measure the contents of 10 bottles of
cough syrup. The results (in fluid ounces) are shown to the
right. 4.218 4.299 4.255 4.248 4.184 4.296 4.265 4.246 4.228 4.232
Assume the sample is taken from a normally distributed population.
Construct 95% confidence intervals for (a) the population
variance sigma squared and (b) the population standard deviation
sigma. Interpret the results.
You randomly select and measure the contents of 1010 bottles of cough syrup. The results (in...
You randomly select and measure the contents of 1010 bottles of
cough syrup. The results (in fluid ounces) are shown. 4.2134.213
4.2954.295 4.2514.251 4.2414.241 4.1844.184 4.2054.205 4.2684.268
4.2454.245 4.2234.223 4.2354.235 Assume the sample is taken from a
normally distributed population. Construct 9898% confidence
intervals for (a) the population variance sigmaσsquared2 and (b)
the population standard deviation sigmaσ. (a) The confidence
interval for the population variance is left parenthesis nothing
comma nothing right parenthesis .0.0004250.000425,0.0044060.004406.
(Round to six decimal places as...
You randomly select and measure the contents of 1010 bottles of cough syrup. The results (in...
You randomly select and measure the contents of 1010 bottles of
cough syrup. The results (in fluid ounces) are shown. 4.2134.213
4.2954.295 4.2514.251 4.2414.241 4.1844.184 4.2054.205 4.2684.268
4.2454.245 4.2234.223 4.2354.235 Assume the sample is taken from a
normally distributed population. Construct 9898% confidence
intervals for (a) the population variance sigmaσsquared2 and (b)
the population standard deviation sigmaσ. (a) The confidence
interval for the population variance is left parenthesis nothing
comma nothing right parenthesis .,. (Round to six decimal places
as...
You randomly select and measure the contents of 10 bottles of cough syrup. The results (in...
You randomly select and measure the contents of
10 bottles of cough syrup. The results (in fluid ounces) are
shown to the right.
4.213
4.293
4.252
4.242
4.183
4.293
4.265
4.243
4.226
4.235
Assume the sample is taken from a normally distributed
population. Construct 95%
confidence intervals for (a) the population variance
σ^2
and (b) the population standard deviation
σ.
Interpret the results.
A sample of 20 glass bottles of a particular type was selected, and the internal pressure...
A sample of 20 glass bottles of a particular type was selected,
and the internal pressure strength of each bottle was determined.
Consider the following partial sample information.
median = 202.7
lower fourth = 197.0
upper fourth = 217.5
Three smallest observations
125.6
187.9
194.1
Three largest observations
220.1
230.1
251.1
(a)
Are there any outliers in the sample?
Yes/No
Any extreme outliers?
Yes/No
(b)
Construct a boxplot that shows outliers.
Comment on any interesting features.
There is a bit...
Suppose a random sample of size 50 is selected from a population with σ = 8....
Suppose a random sample of size 50 is selected from a population
with
σ = 8.
Find the value of the standard error of the mean in each of the
following cases. (Use the finite population correction factor if
appropriate. Round your answers to two decimal places.)
(a)
The population size is infinite.
(b)
The population size is
N = 50,000.
(c)
The population size is
N = 5,000.
(d)
The population size is
N = 500.
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