20.
You use the finite population correction factor when
A.
you sample without replacement and the sample size is larger than 5% of the population
size.
B.
you sample without replacement and the sample size is smaller than 5% of the population
size.
C.
you sample with replacement and the sample size is larger than 5% of the population size.
D.
you sample with replacement and the sample size is smaller than 5% of the population size.
PART B: PROBLEM SOLVING QUESTIONS (10 Marks Each)
1.
The table below contains the opinions of a sample of 200 people broken down by gender about the
latest congressional plan to eliminate anti-trust exemptions for professional baseball.
For
Neutral
Against
Totals
Female
38
54
12
104
Male
12
36
48
96
Totals
50
90
60
200
a)
Construct a table of row percentages.
2 marks
b)
Of those for the plan in the sample, what percent were females?
2 marks
c)
Of the females in the sample, what percent were either neutral or against?
2 marks
d)
What percent of the 200 were males who were neutral?
2 marks
e)
Assuming the sample is a good representation of the population, what percent of the females in the
population is expected to be not against the plan?
2 marks
Answers
a)
For
Neutral
Against
Totals
Female
36.54
51.92
11.54
100.00
Male
12.50
37.50
50.00
100.00
Totals
25.00
45.00
30.00
100.00
b)
76
c)
63.46 or (51.92 + 11.54)
d)
18
e)
88.46 or (36.54 + 51.92)
2.
In a recent academic year, many public universities in the United States raised tuition and fees due to
a decrease in state subsidies. The change in the cost of tuition, a shared dormitory room, and the
most popular meal plan from the previous academic year for a sample of 10 public universities were
as follows: $1,589, $593, $1,223, $869, $423, $1,720, $708, $1,425, $922 and $308.
a)
What is the mean and median change in the cost?
2 marks
b)
What is the standard deviation of the change in the cost?
2 marks
c)
What is the interquartile range of the change in the cost?
2 marks
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STAT101, Midterm Test
5
d)
What is the coefficient of variation of the change in cost?
1 mark
e)
Is the change in the cost right- or left-skewed?
2 marks
f)
If kurtosis statistic of the change in the cost is -1.32, is the change in the cost lepokurtic or
platykurtic?
1 mark
Answers
a)
$978, $895.5
b)
$491.8
c)
$832
d)
50.29%
e)
right-skewed
f)
platykurtic
3.
According to the record of the registrar's office at a state university, 35% of the students are
freshman, 25% are sophomore, 16% are junior and the rest are senior. Among the freshmen,
sophomores, juniors and seniors, the portion of students who live in the dormitory are, respectively,
80%, 60%, 30% and 20%.
a)
What is the probability that a randomly selected student is a sophomore who does not live in a
dormitory?
2 marks
b)
What is the probability that a randomly selected student is a junior or senior who lives in a
dormitory?
2 marks
c)
What percentage of the students live in a dormitory?
2 marks
d)
If a randomly selected student lives in the dormitory, what is the probability that the student is not a
freshman?
2 marks
e)