QUIZ IV BIT 2405 Solutions
A random sample of 16 students selected from the student body of a large university had an average age of 25 years. We
want to determine if the average age of all the students at the university is significantly different from 24. Assume the
distribution of the population of ages is normal with a standard deviation of 2 years.
1. The correct set of hypotheses is
1.
H
0
:
p
24 H
a
:
p
≠
24
2.
H
0
:
25 H
a
:
≠
25
3.
H
0
:
24 H
a
:
≠
24
4.
None of the above
2. The test statistic is
1.
1.96
2.
2.00
3.
1.645
4.
0.05
null
the
reject
to
Fail
t
t
t
t
t
2
/
2
/
2
/
;
131
.
2
;
2
4
2
24
25
3. At a .05 level of significance, it can be concluded that the mean age is
1.
not significantly different from 24
2.
significantly different from 24
3.
significantly less than 24
4.
significantly less than 25
A random sample of 100 people was taken. Eighty of the people in the sample favored Candidate A. We are
interested in determining whether or not the proportion of the population in favor of Candidate A is
significantly more than 75%.
4.
The
p
value is
1.
0.2112
2.
0.05
3.
0.025
4.
None of the above
H
0
: p
≤
.75 H
a
: p > .75
15
.
1
100
25
.
72
.
75
.
8
.
0
z
;
1251
.
)
(
0
z
Z
P
value
p
reject
to
fail
05
.
1251
.
5. At a .05 level of significance, it can be concluded that the proportion of the population in favor of candidate
A is
1.
significantly greater than 75%
2.
not significantly greater than 75%
3.
significantly greater than 80%
4.
not significantly greater than 80%
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Problems 68
In order to determine the average price of hotel rooms in Atlanta, a sample of 64 hotels was selected. It was
determined that the average price of the rooms in the sample was $112. The population standard deviation is
known to be $16. Use a 0.05 level of significance and determine whether or not the average room price is
significantly different from $108.50.
6. The correct set of hypotheses is
1.
H
0
:
≥
108.50 H
a
:
≠
108.50
2.
H
0
:
≤
108.50 H
a
:
>
108.50
3.
H
0
:
108.50 H
a
:
≠
108.50
4.
H
0
:
112 H
a
:
≠
112
7. The test statistic is
1.
1.75
2.
1.75
3.
1.645
4.
0.05
2
/
;
75
.
1
64
16
50
.
108
112
z
z
1.96; 1.96 < 1.75 < 1.96
8. At a .05 level of significance,
1.
do not reject H
0
, there is not sufficient evidence at
α
.05 to conclude that the
average room price is significantly different from $108.50
2.
Reject H
0
, there is not sufficient evidence at
α
.05 to conclude that the
average room price is significantly different from $108.50
3.
Reject H
0
, there is sufficient evidence at
α
.05 to conclude that the average
room price is significantly different from $108.50
4.
None of the above
9. A carpet company advertises that it will deliver your carpet within 15 days of purchase. A sample of 49 past customers
is taken. The average delivery time in the sample was 16.2 days. Assume the population standard deviation is known to be
5.6 days. Give the pvalue and the decision
1.
0.0668; there is not sufficient evidence at
α
.05 to conclude that the average
delivery time is more than what is advertised
2.
0.0668; there is sufficient evidence at
α
.05 to conclude that the average
delivery time is more than what is advertised
3.
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 Spring '08
 PLKitchin
 Normal Distribution, Standard Deviation, sufficient evidence, Wireless Phone

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