# Introduction to Statistics Sample Exam Chapters 1 - 4

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```					                                Introduction to Statistics
Sample Exam Chapters 1 - 4
1. To estimate the percentage of Regis College students who use illegal drugs, a uniformed police oﬃcer
used illegal drugs in the last month. She continued asking students until she had 40 responses.
(a) What is the population for this survey?

(b) What is the sample for this survey?

(c) What factors make this survey subject to bias?

(d) Describe another way of collecting the data, and mention at least one advantage and at least one

2. Fairﬁeld College is considering a new course evaluation form for all the classes taught on campus. One
concern is the amount of time necessary to ﬁll out the form. A random sample of 30 students were
asked to ﬁll out the form for the class they had at 10:00 a.m. The times in minutes to ﬁll out the form
were as follows:
18 19 8 12 18 20 15 17 19 23
22 30 21 16 44 17 15 12 18 26
51 23 35 31 42 5                2   3     9 12
Compute the ﬁve number summary and make a box and whisker plot for this data. Be sure to indicate
the scale.

Describe the shape of the display; is it skewed one way or the other?

3. The Richter scale is used to measure the magnitude of earthquakes. A sample of 15 earthquakes
occurring in the United States had Richter scale ratings of

6.0     2.1   1.3   5.1   3.4   2.1    1.4    1.5
2.0     3.1   4.6   1.2   1.8   2.7    3.5

Compute the ﬁve number summary and the interquartile range. Make a box and whisker plot. Is this
data skewed right or left?

4. We wish to make a histogram representing the following data.

63    21    13   51    34    21    14     15
20    31    46   12    18    27    35      4
34    24    54   10    15    22    18     42

If we wish the histogram to have 6 bars, what should the class width be?
5. The frequency table for the data in problem 4 above is shown below. Fill in the blank entries.

Class Limits   Class Boundaries    Midpoint        Freq.   Rel. Freq.   Cumulative Freq
8.5             4      16.7%             4

9        37.5%

3                         16

4        16.7%            20

6. The histogram below shows the frequencies of the number of houses sold in a month by a particular
realty company.

Use the information from the histogram to compute the sample mean and sample standard deviation.

7. The Richter scale is used to measure the magnitude of earthquakes. A sample of 6 earthquakes occurring
in the United States had Richter scale ratings of

6.0   2.1   1.3   5.1     3.4   2.1

Compute the sample mean and standard deviation for this data.
8. A population of golﬁsh in a large ﬁsh tank was studied and the mean length was found to be 6
centimeters with a standard deviation of 1.1 cm. A separate study looked at the lengths of sharks
found in ﬁshermen’s nets. This second study found that the mean length of the sharks measured was
8 feet with a standard deviation of 2.1 feet.
Compute the coeﬃcient of variation for the length of goldﬁsh and for the length of sharks.

Which data set is more spread out?

A sample of a trout population from a lake was measured and the mean length was found to be 8
inches with a standard deviation of 1.5 inches. Is the distribution of lengths of trout more like the
distribution of lengths of goldﬁsh or the distribution of lengths of sharks? Explain.

9. (a) Find a Chebyshev interval which will contain at least 75% of the lengths of trout in the previous
problem.
(b) Find a Chebyshev interval which will contain at least 88.9% of the lengths of sharks in the previous
problem.
(c) Find a Chebyshev interval which will contain at least 93.8% of the lengths of goldﬁsh in the
previous problem.

10. Is the data represented by the following box and whisker plot skewed left or right?

10     15    20     25     30    35     40     45

(True or False) More than half of the data is larger than the median.

(True or False) Exactly half of the data is inside the box.

(True or False) The left whisker represents the ﬁrst quartile.

(True or False) There is more data in the right whisker than in the left whisker.

11. We’ve got 20 cookies in a jar. There are 14 chocolate chip and 6 oatmeal raisin. If you draw one
cookies at random from the jar, what is the probability that it is oatmeal raisin?

12. In another cookie jar we have 6 chocolate chip, 4 oatmeal raisin, and 3 sugar cookies. If you take one
cookie at random out of this jar, what is the probability that it is either oatmeal raisin or a sugar
cookie? Are these mutually exclusive events?

13. In yet another cookie jar we have

10 chocolate chip cookies, 3 of which are burnt,
12 oatmeal raisin, 5 or which are burnt, and
9 sugar cookies, 4 of which are burnt.

If you draw one cookie at random from this jar, what is the probability that it is either a sugar cookie
or a burnt cookie (of any kind). Are these events mutually exclusive?
14. If we draw one cookie from the jar in problem 11, and one cookie from the jar in problem 12, what is
the probability that they are both chocolate chip?

15. The results of an extensive medical study to determine the eﬃcacy of a new medical test for a common
medical condition are summarized in the following table.

Condition      Condition
Present        Absent       Row Total
Test Result +      63             96           159
Test Result -      252           564           816
Column Total       315           660           975

Find
(a) P (A),
(b) P (A, given +),
(c) P (+),
(d) P (P and +),
(e) P (+ given P )
(f) P (+ given A)

Mean and Standard Deviations:

x               (x − x)2
Sample Data      x=     n       s=          n−1

xf             (x − x)2 f
Grouped Data     x=     n       s=       n−1
n=     f

Chebyshev Intervals:

at least 75%    µ − 2σ to µ + 2σ

at least 88.9%   µ − 3σ to µ + 3σ

at least 93.8%   µ − 4σ to µ + 4σ

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