Question
In: Math
The mean caffeine content μ of a certain energy drink is under examination. A measure taken...
The mean caffeine content μ of a certain energy drink is under examination. A measure taken on a random sample of size n = 16 yieldsx̄ = 2.4 g/l.
-
(a) Assuming that the standard deviation is known to be σ = 0.3, find the 95 confidence interval for μ.
-
(b) If that the standard deviation is unknown but the sample standard deviation is s = 0.3, find the 95 confidence interval for μ.
Solutions
milcah answered 1 year agoRelated Solutions
In the caffeine extraction from an energy drink lab: a. Why was it necessary to extract...
In the caffeine extraction from an energy drink lab:
a. Why was it necessary to extract the caffeine from the energy
drink? Why could we not have sublimated the energy drink directly
as a solution?
b. Why did we extract the energy drink with dichloromethane,
specifically, and not another organic solvent such as methanol or
hexane?
A new energy drink on the market is widely marketed as “caffeine-free”. Based on the nature...
A new energy drink on the market is widely marketed as
“caffeine-free”. Based
on the nature of complaints filed by several consumers, it
appears that the “
caffeine-free” claim might actually be fraudulent. You are
given the
responsibility of examining this issue. How would you go about
your task of
verifying the validity of the “caffeine-free” label? Explain
your strategy clearly.
One 16-ounce bottle of an energy drink has an average of 400 mg of caffeine with...
One 16-ounce bottle of an energy drink has an average of 400 mg
of caffeine with a standard deviation of 20 mg. What is the
probability that the average caffeine in a sample of 25 bottles is
no more than 390 milligrams?
a) 0.006
b) 0.004
c) 0.002
d) 0.001
A survey of 16 energy drinks noted the caffeine concentration of each drink in milligrams per...
A survey of 16 energy drinks noted the caffeine concentration of
each drink in milligrams per ounce. The results are given in the
table below.
Concentration of caffeine (mg/oz)
9.1 8.9 7.4 7.8 7.7 8.9 8.9 9.0 9.0 9.1 8.2 9.0 9.2 8.1 8.6
9.0
Find the mean and sample standard deviation of these data. Round
to the nearest hundredth.
A. mean
B. sample standard deviation
A manufacturer claims that the average tar content of a certain kind of cigarette is μ...
A manufacturer claims that the average tar content of a certain
kind of cigarette is μ = 14.0. In an attempt to show that it
differs from this value, five measurements are made of the tar
content (mg per cigarette):
14.5
14.2
14.4
14.3
14.6
Construct a 99% confidence interval for the variance of the
population sampled.
The mean potassium content of a popular sports drink is listed as 146 mg in a...
The mean potassium content of a popular sports drink is listed
as 146 mg in a 32-oz bottle. Analysis of 28 bottles indicates a
sample mean of 145.5 mg.
(a)
State the hypotheses for a two-tailed test of the claimed
potassium content.
a.
H0: μ = 146 mg vs. H1:
μ ≠ 146 mg
b.
H0: μ ≤ 146 mg vs. H1:
μ > 146 mg
c.
H0: μ ≥ 146 mg vs. H1:
μ < 146 mg
a
b...
Enthalpy H is a measure of the energy content of a system at constant pressure. Chemical...
Enthalpy H is a measure of the energy content of a system at
constant pressure. Chemical reactions involve changes in enthalpy,
ΔH, which can be measured and calculated:
ΔHrxn∘=∑productsmΔHf∘−∑reactantsnΔHf∘ where the subscript "rxn" is
for "enthalpy of reaction" and "f" is for "enthalpy of formation"
and m and n represent the appropriate stoichiometric coefficients
for each substance. The following table lists some enthalpy of
formation values for selected substances. Substance ΔHf∘ (kJ/mol)
NaOH(aq) −469.1 MgCl2(s) −641.8 NaCl(aq) −407.3 Mg(OH)2(s) −924.5...
The caffeine content of a cup of coffee in the cafeteria is a normally distributed random variable with μ = 130 mg and σ = 30 mg.
The caffeine content of a cup of coffee in the cafeteria is a normally distributed random variable with μ = 130 mg and σ = 30 mg.
What is the probability that a randomly chosen cup of coffee will have more than 130 mg?
Less than 100 mg?
Between 90 mg and 150 mg?
If the cup of coffee was the strongest 5% in caffeine content (hint: think about whether this would be above or below the mean), how many...
A company that makes cola drinks states that the mean caffeine content per 12-ounce bottle of...
A company that makes cola drinks states that the mean caffeine
content per 12-ounce bottle of cola is 35 milligrams. You want to
test this claim. During your tests, you find that a random sample
of thirty 12-ounce bottles of cola has a mean caffeine content of
35.7 milligrams. Assume the population is normally distributed and
the population standard deviation is 7.4 milligrams. At α=0.01,
can you reject the company's claim? Complete parts (a) through
(e).
(a) Identify H0 and...
A company that makes cola drinks states that the mean caffeine content per 12-ounce bottle of...
A company that makes cola drinks states that the mean caffeine
content per 12-ounce bottle of cola is 55 milligrams. You want to
test this claim. During your tests, you find that a random sample
of thirty 12-ounce bottles of cola has a mean caffeine content of
53.4 milligrams. Assume the population is normally distributed and
the population standard deviation is 7.2 milligrams. At
alphaequals0.02, can you reject the company's claim? Complete
parts (a) through (e). (a) Identify Upper H...
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