Cigarette Tar
1
.
21
:
≥
μ
o
H
The mean amount of tar in 100mm filtered cigarettes is
≥
21.1 mg.
1
.
21
:
<
μ
a
H
The mean amount of tar in 100mm filtered cigarettes is < 21.1 mg. CLAIM
Given:
_
x
= 13.2 mg
μ
= 21.1 mg
s = 3.7 mg
n = 25
α
= .05
Left-tailed test
n
s
x
t
μ
0
−
=
= -10.67 (Test Stat.)
Critical Value = -1.711
Conclusion: Reject null.
At the
α
= .05 significance level the data provide sufficient evidence
to reject the null hypothesis that the mean amount of tar in 100 mm filtered cigarettes is 21.1 mg.
Retain
T.S: -10.67
CV = -1.711
Reject

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ANSWER KEY
Problem 24.2:
Toxic Mushrooms:
Cadmium, a heavy metal, is toxic to animals.
Mushrooms, however, are able to absorb it and accumulate
cadmium at high concentrations.
The Czech and Slovak governments have set a safety level for cadmium in dry vegetables at
0.5 parts per million (ppm).
A sample of 12
Boletus piniletus pinicola
mushrooms has a mean cadmium level of .53 ppm and a
standard deviation of 0.37 ppm.
At the
α
= .05 significance level, do the data provide sufficient evidence to conclude that the
mean cadmium level in
Boletus piniletus pinicola
mushrooms is greater than the government’s recommended limit of .5 ppm?
Toxic Mushrooms
5
.
:
≤
μ
o
H
The safe level of cadmium in Boletus mushrooms is .5ppm
CLAIM
5
.
:
>
μ
a
H
The level of cadmium in Boletus mushrooms exceeds .5 ppm
Given:
_
x
= .526 ppm
μ
= .5 ppm
σ
= .37 ppm
n = 12
α
= .05
Right-tailed test
n
x
z
σ
μ
0
−
=
= .2808 (Test Stat.)
Critical Value = 1.645
Conclusion: Fail to reject.
At the
α
= .05 significance level the data do not provide
sufficient evidence to conclude that the mean cadmium level in Boletus pinicola mushrooms
is greater than the government recommended limit of .5 ppm.
Problem 24.3
Acid Rain and Lake Acidity:
Acid rain from the burning of fossil fuels has caused many lakes around the world to become
acidic.
A lake is classified as non-acidic if it has a pH greater than 6.
Scientists obtained water samples from 15 high
mountain lakes in the Southern Alps.
The mean pH of these lakes was 6.6 with a standard deviation was 0.672.
At the
α
= .05
significance level,
do the data provide sufficient evidence that, on average, high mountain lakes in the Southern Alps are non-
acidic (i.e., greater than a pH of 6)?
Retain
T.S: .2808
C.V.1.645
Reject

43

ANSWER KEY
44

ANSWER KEY
45
25
4.21.2016
STAT 101
TOPICS: Hypothesis Testing
DOCUMENTS:
•
HANDOUTS:
Orange #25
•
AVAILABLE ONLINE:
Orange #25
HWK:
•
Problems from green #24 and this sheet
FORMULAS:
Hypothesis Testing:
n
x
z
σ
μ
0
−
=
n
s
x
t
μ
0
−
=
n
pq
p
p
z
−
=
^
NEXT CLASS:
Exam II review; CA#8 (if not already submitted)
Statistics Essentials:
Know: 1) how to write hypotheses in statistical format and in written format; 2) what statistical
significance means; 3) what terms associated with hypothesis testing mean – e.g. critical value(s), test statistic, p value, etc.; 4)
how to conduct a hypothesis test and interpret the results.