# What is Statistics?

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proggerardo
School: Boston College

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STAT 200
OL4 / US2 Sections
Final Exam
Spring 2018
1. QUESTION 1
a) ITEM A.
True. The intersection of A and B, P(A AND B), consists of outcomes that are in both A and
B. The union of A and B, P(A OR B), consists of outcomes that are in A or B or both.
b) ITEM B.
False. The statistic variance only measures the dispersion of a data set from its mean value.
A variance with a value of 0 implies that all the values are equal to the mean but not
necessary, all data must be zero.
c) ITEM C.
False. The volume of milk can be fractional with a continuous and infinite number of
possibilities (quantitative continuous variable).
d) ITEM D.
True. The standard deviation is the statistic that show how spread are the values from the
mean. The more spread out a data distribution is, the greater its standard deviation.
e) ITEM E.
False. The P-value of this case is 0.03 and it’s lower than the level of significance, supporting
that there is enough evidence to reject the null hypothesis and accept the alternative
hypothesis.

2. QUESTION 2.
(i) Statistic
A statistic is a numerical summary of a sample (100 students graduated from UMUC in
2016) taken from the population (students graduated from UMUC in 2016).
(iii) Ordinal
An ordinal scale classifies data into a rank of categories (from 0 to 5 stars).
(iii) Systematic
The systematic sampling is also called interval sampling, meaning that is an interval
between the units selected for the study.

3. QUESTION 3
a) ITEM A.
IQ Scores 50-69
25
𝐶𝑅𝐹 =
= 0.025
1000
IQ Scores 70-89
25
250
275
𝐶𝑅𝐹 =
+
=
= 0.275
1000 1000 1000
IQ Scores 90-109
25
250
𝑥
725
𝐶𝑅𝐹 =
+
+
=
= 0.725
1000 1000 1000 1000
𝑥 = 450
Total Frequency
𝑇𝐹 = 1000 = 25 + 250 + 450 + 𝑥 + 27
𝑥 = 248
IQ Scores 110-129
25
250
450
248
973
𝐶𝑅𝐹 =
+
+
+
=
= 0.973
1000 1000 1000 1000 1000
IQ Scores 130-149
25
250
450
248
27
1000
𝐶𝑅𝐹 =
+
+
+
+
=
= 1.000
1000 1000 1000 1000 1000 1000
b) ITEM B.
450
248
𝑃(%) = 𝑃90−119 + 𝑃120−139 = (
+
) × 100 = 69.8
1000 1000
c) ITEM C.
The median of this distribution is in the group with an IQ score between 90-109. The median
is the middle value of the observations when the observations are ordered from the smallest
to the largest. In this case, the group where the cumulative frequency of 0.500 is located.

4. QUESTION 4.
a) ITEM A.
The range is the difference between the largest and the smallest observations.
𝑅 = 100 − 15 = 85
(iii) 45 – 65
This group of scores between 45 and 65 include the first and the second quartile, meaning
that there is at least 25% of the sample (50 students); also, includes the group of scores
between 45 and 55, a group in common with the score band of 35-55, making the comparison
between the bands of 35-45 and 55-65 for the options (ii) and (iii). The option (i) is discarded
because it doesn’t have a quartile, meaning that the number of students is less than 50
students.
(iii) 50
Between 65 (second quartile) and 85 (third quartile) there is the 25% of the sample (50
students).

5. QUESTION 5.
a) ITEM A.
P(A) = The first selected card is an ace
P(B) = The second selected card is an ace
With replacement means that in the second event, the number total aces and cards will be the
same as the first event.
𝑃(𝐴 ∩ 𝐵) = 𝑃(𝐴) × 𝑃(𝐵) =

4
4
16
×
=
= 0.0059
52 52 2704

b) ITEM B.
Without replacement means that in the second event, the number total aces will be 3 and cards
will be 51.
𝑃(𝐴 ∩ 𝐵) = 𝑃(𝐴) × 𝑃(𝐵) =

4
3
12
×
=
= 0.0045
52 51 2652

6. QUESTION 6.
a) ITEM A
The event (S OR P) means the situation where the randomly selected student takes STAT200
or PSYC300.
b) ITEM B.
300
= 0.300
1000
150
𝑃(𝑃) =
= 0.150
1000
50
𝑃(𝑆 ∩ 𝑃) =
= 0.050
1000
𝑃(𝑆) =

𝑃(𝑆 ∪ 𝑃) = 𝑃(𝑆) + 𝑃(𝑃) − 𝑃(𝑆 ∩ 𝑃) =

300
150
50
400
+

=
= 0.400
1000 1000 1000 1000

7. QUESTION 7.
a) ITEM A.
There are three possibilities to have a sum of exactly 6 after two rolls: 2+4, 4+2, and 3+3.
3
𝑃(𝐴) =
= 0.083
36
There are three possibilities to have an even number when the dice is rolled first.
3
𝑃(𝐵) = = 0.500
6
If the first dice is an even number, the possibilities to have a sum of exactly 6, after two rolls,
reduced to two events: 2+4, and 4+2.
2
𝑃(𝐴 ∩ 𝐵) =
= 0.056
36
b) ITEM B.
No. The variables are dependent, the multiplication rule is not met.
𝑃(𝐴)𝑃(𝐵) = 0.083 × 0.50...

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Anonymous
Thanks for the help.

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