Download MTH 345 Exam 4 Fall 2013 Justify all answers with neat

MTH 345
Exam 4
Fall 2013
Justify all answers with neat and organized work. Clearly indicate your answers.
For hypothesis tests, you must use the required format. 100 points possible.
1. (11 pts.) Examine the given statement, then follow the first three steps of the
procedure for a hypothesis test.
When parents use the XSORT method of gender selection, the proportion of baby
girls is greater than 0.5.
1. Original claim in symbolic form:
2. Competing idea in symbolic form:
3. H0 :
H1 :
2. (11 pts.) Examine the given statement, then follow the first three steps of the
procedure for a hypothesis test.
The mean pulse rate (in beats per minute) of adults is 76 or lower.
1. Original claim in symbolic form:
2. Competing idea in symbolic form:
3. H0 :
H1 :
3. (18 pts.) The drug Symbicort is used to treat asthma. In a clinical trial of
Symbicort, 18 of 277 treated subjects experienced headaches (based on data from
AstraZeneca). Use a 0.05 significance level to test the claim that the percentage of
treated subjects that experienced headaches is different from 10%. Use the P -Value
Method.
Hypothesis Test: P -Value Method
1. Original claim in symbolic form:
2. Competing idea in symbolic form:
3. H0 :
H1 :
4. α =
5. Formula for the test statistic:
6. Observed value of the test statistic, with calculations:
Graph showing observed value of the test statistic and P -value:
P -value:
7. Reject H0 / Fail to reject H0 (Circle one)
8. Wording of final conclusion in simple, nontechnical terms, addressing the
original claim:
4. (18 pts.) A study was conducted to determine the proportion of people who
dream in black and white instead of color. Among 306 people over the age of 55, 68
dream in black and white, and among 298 people under the age of 25, 13 dream in
black and white (based on data from “Do We Dream in Color?” by Eva Murzyn,
Consciousness and Cognition, Vol. 17, No. 4). Use a 0.01 significance level to test
the claim that the porportion of people over 55 who dream in black and white is
greater than the proportion for those under 25. Use the Traditional (i.e., Critical
Value) Method.
Hypothesis Test: Traditional Method (i.e., Critical Value Method)
1. Original claim in symbolic form:
2. Competing idea in symbolic form:
3. H0 :
H1 :
4. α =
5. Formula for the test statistic:
6. Observed value of the test statistic, with calculations:
Graph showing critical value(s) and critical region:
Critical value(s):
7. Reject H0 / Fail to reject H0 (Circle one)
8. Wording of final conclusion in simple, nontechnical terms, addressing the
original claim:
5. (18 pts.) A study was conducted to investigate some effects of physical training. Sample data are listed below (modified from data from “Effect of Endurance
Training on Possible Determinants of VO2 During Heavy Exercise,” by Casaburi et
al., Journal of Applied Physiology, Vol. 62, No. 1). At the 0.05 level of significance,
test the claim that training reduces weight. All weights (masses, really) are given
in kilograms.
Subject
A
B
C
D
E
Pre-training
77
59
92
70
85
Post-training
76
58
88
70
84
Hypothesis Test: Traditional Method (i.e., Critical Value Method)
1. Original claim in symbolic form:
2. Competing idea in symbolic form:
3. H0 :
H1 :
4. α =
5. Formula for the test statistic:
6. Observed value of the test statistic, with calculations:
Graph showing critical value(s) and critical region:
Critical value(s):
7. Reject H0 / Fail to reject H0 (Circle one)
8. Wording of final conclusion in simple, nontechnical terms, addressing the
original claim:
6. (4 pts.) A hypothesis test will be conducted of the claim “more than 75%
of people do not open unfamiliar email and instant-message links.” Which of the
following statements best expresses the type I error for this test?
A. We conclude that more than 75% of people do not open unfamiliar email and
instant-message links, when the percentage of people who do not open unfamiliar
email and instant-message links actually is more than 75%.
B. We conclude that 75% of people do not open unfamiliar email and instantmessage links, when the percentage of people who do not open unfamiliar email
and instant-message links actually is 75%.
C. We conclude that 75% of people do not open unfamiliar email and instantmessage links, when the percentage of people who do not open unfamiliar email
and instant-message links actually is more than 75%.
D. We conclude that more than 75% of people do not open unfamiliar email and
instant-message links, when the percentage of people who do not open unfamiliar
email and instant-message links actually is 75%.
7. (4 pts.) A hypothesis test will be conducted of the claim “the mean age of
all race car drivers is equal to 30 years.” Which of the following statements best
expresses the type I error for this test?
A. We conclude that the mean age of all race car drivers is not equal to 30 years,
when the mean age of all race car drivers actually is not equal to 30 years.
B. We conclude that the mean age of all race car drivers is equal to 30 years, when
the mean age of all race car drivers actually is not equal to 30 years.
C. We conclude that the mean age of all race car drivers is not equal to 30 years,
when the mean age of all race car drivers actually is equal to 30 years.
D. We conclude that the mean age of all race car drivers is equal to 30 years, when
the mean age of all race car drivers actually is equal to 30 years.
8. (18 pts.) A sample of 25 filtered 100-mm cigarettes is obtained, and the tar
content of each cigarette is measured. The sample has a standard deviation of 3.7
mg (based on data from the Federal Trade Commission). (Assume that a simple
random sample is selected from a normally distributed population.) Use a 0.05
significance level to test the claim that the tar content of filtered 100-mm cigarettes
has a standard deviation different from 3.2 mg. Use the Traditional (i.e., Critical
Value) Method.
Hypothesis Test: Traditional Method (i.e., Critical Value Method)
1. Original claim in symbolic form:
2. Competing idea in symbolic form:
3. H0 :
H1 :
4. α =
5. Formula for the test statistic:
6. Observed value of the test statistic, with calculations:
Graph showing critical value(s) and critical region:
Critical value(s):
7. Reject H0 / Fail to reject H0 (Circle one)
8. Wording of final conclusion in simple, nontechnical terms, addressing the
original claim:
Formulas
Ch. 8: Test Statistics (one population)
p̂ − p
Proportion—one population
z= pq
n
p̂ =
z=
x−μ
√ Mean—one population (σ known)
σ/ n
t=
x−μ
√ Mean—one population (σ unknown)
s/ n
χ2 =
x
n
(n − 1)s2
Standard deviation or variance—one population
σ2
Ch. 9: Test Statistics (two populations)
z=
t=
(p̂1 − p̂2 ) − (p1 − p2 )
Two proportions
p̄q̄
p̄q̄
+
n1
n2
p̄ =
x1 + x2
n1 + n2
(x1 − x2 ) − (μ1 − μ2 )
(df = smaller of n1 − 1 and n2 − 1)
s22
s21
+
n1
n2
Two means—independent; σ1 and σ2 unknown, and not assumed equal.
t=
d − μd
√ Two means—matched pairs (df = n − 1)
sd / n