BSTA 200 Test 1 Review
Round all monetary values to 2 decimal places
1) Identify each number as discrete or continuous.
a) The altimeter on a Air Canada jet indicates a height of 7200 metres.
b) Radar indicated that race car driver Paul Tracey reached a speed of 245 km/h on the
straight away.
c) There are 6150 students at the Lakeshore Campus.
d) In a survey of 1000 people 930 recognized the Campbell’s Soup label.
e) Based on the math Centre research, a student spends 2.5 hours amound those visited.
f) BSTA 200 average score in midterm 1 is 69%.
g) BSTA 200 text book has 350 pages.
2) Determine which of the four levels of measurement is most appropriate (nominal, ordinal,
interval, or ratio).
a) Ratings of good, satisfactory or unsatisfactory for a new breakfast cereal.
b) Social insurance number
c) Year in which the Toronto Maple Leafs won the Stanley Cup.
d) Annual income of nurses
e) Ranking of Humber College services in terms of students visits.
f) Page number found on BSTA 200 textbook.
g) Attendance records of Math Centre.
h) Temperature of Toronto in Summer.
3) Define the following: Mean, Frequency, Standard Deviation, Correlation.
4) Define the following: Statistics, Descriptive Statistics, and Statistical Inference.
5) A statistics student gathers information on what time would be preferred for a body blast
exercise program. Which measure of central tendency should be used to summarize this
data?
6) The same student gathers information on the number of hours doing statistics homework.
Which measure of central tendency should be used to summarize this data?
7) The Math Centre collects information during the Winter Semester to find out which school
represents highest number of students visiting them which measure of central tendency
should be preferred to use?
8) The following are the March electric bills (to the nearest dollar) for a sample of 12 similarly
sized houses: $212, $191, $176, $149, $182, $92, $108, $138, $153, $167, $225 and $194.
a) Calculate the mean, median, and mode.
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BSTA 200 Test 1 Review
Round all monetary values to 2 decimal places
b) Which measure of central tendency would be the best for this data? Why?
c) Calculate the value of P40 , D6 , and Q3
d) Calculate the standard deviation and variance.
e) Calculate the coefficient of skewness and comment on the shape of this distribution.
9) The following are midterm scores obtained by ten students appeared in the test centre in
the final test. The full mark is 100.
0, 70, 30.5, 91, 100, 29, 83, 55, 38, 55
a) Calculate the mean, median, and mode
b) Calculate the value of P45 , D2 , and Q1 .
c) Calculate the standard deviation and variance.
d) Calculate the coefficient of skewness and comment on the shape of this distribution.
10) Find out the weighted arithmetic mean Questions asked by a student the following table
shows students asked different number of questions to tutors at the Math Centre.
Questions Asked Number of Students
8
13
7
7
5
12
3
20
1
25
0
3
11) A stockbroker placed the following order for a customer: 50 shares of Alcan Aluminum
preferred at $104 a share, 75 shares of red Lake Gold Mines at $62.50/ share and 20
shares of Scotiabank $58/ share. Want is the weighted arithmetic mean price per share?
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BSTA 200 Test 1 Review
Round all monetary values to 2 decimal places
12) The following data represents the hours overtime worked by employees in a two-week
period at Jose Construction.
5, 11, 12, 19, 14, 21, 13, 8, 29, 22, 22, 16, 24, 6, 1, 3, 6, 24, 16, 28, 35, 10, 38, 30
a) According to ’2k rule’ how many intervals should be used.
b) Construct a frequency distribution with the lower limit of the first interval equal to
0.
c) Construct a relative frequency distribution. What percent worked from 16 to 24 hours
of overtime?
d) Construct a cumulative frequency distribution and sketch on ogive.
e) What percent of the workers worked less than 28 hours of overtime?
f) How many workers worked more than 20 hours overtime?
13) The following is the number of minutes to commute from home to Humber College.
28, 25, 48, 37, 41, 19, 32, 26, 16, 23, 23, 29, 36, 26, 21, 32, 25, 31, 43, 35, 42, 38, 33, 28
(a) According to the 2k rule, how many intervals should be used.
(b) Construct a frequency distribution with the lower limit of the first interval equal to
15.
(c) Construct a relative frequency distribution and sketch an ogive.
(d) What percent of the student commuted less than 25 minutes.
(e) How many students commuted more than 32 minutes.
14) The overtime hours at Jose Construction have a mean of 17.2 hours and a standard
deviation of 10.3 hours. Overtime hours at Batista Construction had a mean of 25.2
hours and a standard deviation of 11.5 hours.
a) Calculate the coefficient of variation and determine which company had a greater
variation in overtime hours?
b) Which company has a greater opportunity to earn extra earnings?
c) Assuming that the distribution of overtime hours is approximately bell shaped forboth
companies calculate the number of hours overtime worked by approximately 95% of
the employees at each firm.
15) A student’s transcript shows an A in a four credit course, an A in a two credit course,
a C in a three credit course, a B in a four credit course and a D in a two credit course.
Grade points are assigned as follows A = 4, B = 3, C = 2, and D = 1. If grade points
are weighted according to the number of credit hours, calculate the grade point average
(weighted mean) to two decimal places.
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BSTA 200 Test 1 Review
Round all monetary values to 2 decimal places
16) Taylor Vacations conducted a survey to gather information on the relationship between
weekly wage and weekly entertainment expense. A random sample of 8 individual produced the following information.
Weekly Wage ($)
800
600
420
280
750
960
400
640
Weekly Entertainment Expense ($)
150
80
50
20
90
160
55
100
(a) What are the dependent variable and the independent variable?
(b) Construct a Scatter Diagram. Does a positive or negative relationship appear to
exist?
(c) Calculate the least squares regression equation and fit it to the scatter diagram.
You may use formulas or the statistical function on the BA II plus.
(d) Calculate the Standard Error of Estimate.
(e) Calculate the coefficient or correlation and the coefficient of determination. Explain
the meaning of each term as they relate to the data.
(f) Predict the weekly entertainment expense if the weekly wage is $560.
(g) If the weekly wage was $1500 could you use the regression equation to predict weekly
entertainment expense? Why?
17) The mean age of the 50 employees at Humber College is 32.6 years and the standard
deviation is 4.4 years. Seneca College has 80 employees and the mean age is 43.3 years
with a standard deviation of 3.9 years.
a) Calculate the coefficient of variation for each group.
b) Determine which employer has the greater variation in age?
c) Suppose that the age distribution for both companies is bell-shaped, calculate the
interval for approximately 95% of the values using the Empirical Rule.
18) Sales Last month at Humber Bookstore were 8 BSTA textbooks each $650, 10 B. Math
textbooks at $825 each, 10 T. Math textbooks at $950 each and 15 CAL100 Textbooks
at $300 each. What was the weighted mean price of textbook sales last month?
19) A financial Analyst is studying the relationship between proce per share and dividends
paid to shareholders. The following table gives the data collected from 8 companies.
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BSTA 200 Test 1 Review
Round all monetary values to 2 decimal places
Company
A
B
C
D
E
F
G
H
Price per Share ($)
20
25
30
38
30
44
50
35
Dividend ($)
3.1
3.3
3.6
8.5
5.5
8.4
8.2
4.5
a) What are the dependent variable and the independent variable?
b) Construct a scatter diagram. Does a positive or negative relationship exist?
c) Calculate the regression equation to predict the dividend paid. You may use the
calculator function as well. Round the regression coefficient to three decimal places.
Show n, Σx, Σx2 , Σy, Σy 2 , Σxy if using a calculator.
d) Calculate the standard error of estimate. (Three decimal places).
e) Determine the coefficient of correlation and the coefficient of determination. (Three
decimal places). Explain the meaning of the coefficient of determination and the
coefficient of correlation as they relate to the price per share and the dividend paid.
f) Predict the dividend paid for a share that cost $35.
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BSTA 200 Test 1 Review
Round all monetary values to 2 decimal places
Answers/Solutions
1) a) Continuous
b) Continuous
c) Discrete
d) Discrete
e) Continuous
f) Continuous
g) Discrete
2) a) Ordinal
b) Nominal
c) Interval
d) Ratio
e) Ordinal
f) Ordinal
g) Ordinal
h) Interval
3) See the definitions
4) See the definitions
5) Mode
6) Mean or Median
7) Mode
8) a) Mean = 165.58 (rounded to 2 decimal places) Medium = 171.50
There is no mode
b) Data appears to be skewed to the left, but not significantly, see e). Either mean or
median can be used.
c) P40 = 155.8
D6 = 180.8
Q3 = 193.25
d) Standard deviation (s) = 39.821
Variance = 1585.712
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BSTA 200 Test 1 Review
Round all monetary values to 2 decimal places
e) Coefficient of skewness = −0.446, the data appears to be negative skewed.
9) (a) Mean = 55.15, Median = 55, Mode = 55
(b) P45 = 54.15
D2 = 29.30
Q1 = 30.125
(c) Standard deviation (s) = 31.4820
Variance = 991.1139
(d) Coefficient of skewness = 0.01429
10) 3.725
11) $76.19/ share
12) a) 5 intervals should be used
b) Frequency distribution: Range = 37, Class width ∼
=8
Class Interval Frequency Relative Frequency Cumulative Frequency
0 to under 8
5
0.2083
5
8 to under 16
6
0.25
11
16 to under 24
6
0.25
17
24 to under 32
5
0.2083
22
32 to under 40
2
0.0833
24
Σ = 24
Σ=1
Cf (%)
20.83
45.83
70.83
91.67
100
c) 25 %
d) Less than cumulative ogive:
e) About 83 %
f) About 14
13) (a) 5 interval should be used
(b)
Class
15-21
22-28
29-35
36-42
43-49
Version 1.8
Frequency
3
8
6
5
2
Σ = 24
Relative Frequency
0.125
0.333333333
0.25
0.208333333
0.083333333
Cumulative Frequency
3
11
17
22
24
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BSTA 200 Test 1 Review
Round all monetary values to 2 decimal places
Class
11
21
28
35
42
49
Cumulative frequency
0
3
11
17
22
24
(c)
(d) About 40%
(e) About 10
14) a) CV: Jose Construction = 59.88
Batista Construction = 45.63
b) Batista Construction
c) Jose Construction = 0 to 37.7 Batista Construction = 2.2 to 48.2
15) 2.933
16) (a) Let weekly wages be the independent variable, scaled as X;
Weekly entertainment expenses be the dependent variable, scaled as Y.
(b) Strong positive correlation.
(c) By financial Calculator, the regression is y’ = 0.202x-34.206
(d) 15.3063
(e) 0.9562
(f) $78.79
(g) No, $1500 is far too outside the range of the data from which the regression equation
has been developed.
17) a) CV = xs × 100%
4.4
Humber → 32.6
× 100% = 13.5%
3.9
Seneca → 43.3 × 100% = 9.01%
b) Humber has a greater variation
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BSTA 200 Test 1 Review
Round all monetary values to 2 decimal places
c)
Using the Empirical Formula:
Humber = 32.6 ± 2(4.4) = 44.4 or 23.8
Seneca = 43.3 ± 2(3.9) = 51.1 or 35.5
18)
Text book
BSTA
B. Math
T. Math
CAL100
TOTAL
Quantity
8
10
10
15
43
Price
650
825
950
300
Total Sales
5200
8250
Weighed Mean Price =
9500
4500
27450
27450
43
= 638.37
19) a) Dividend paid is the independent variable while the price per share is dependent
variable.
b)
It appears to be a strong positive correlation.
c) By Financial Calculator: The regression equation: Y’ = 0.2114x-1.5514
d) The Standard Error of Estimate = 1.228
e) The Coefficient of Correlation, r = 0.8757
The Coefficient of Determination, r2 = 0.7669
f) Y’ = 0.2114x-1.5514 = Y’ = 0.2114(35)-1.5514 = 5.85
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