Download 1 - Beedie School of Business

Sampled Midterm Exam Problems: Hints or Answers (check figures or solutions) provided separately.
NOTE: Because these questions are selected from the old midterm exams, so please ignore the problem
numbering or such as (old#) etc..
__________________________________________
1. The following histogram represents the distribution of acceptance rates (percent accepted) among 25 business
schools in 1995. In each class interval, the left endpoint is included but not the right.
(a) What percent of the schools have an acceptance rate of at least 40%?
(b) One way to estimate the mean of a distribution from a histogram is to assume that all values in a bar have value
equal to its midpoint. Using this method, estimate the average acceptance rate amongst schools that have an
acceptance rate less than 25%.
2. (old5) A sample was taken of the salaries of 5000 employees of a very large company. The following is a boxplot
of the salaries (in thousands of dollars) for this year.
(a) Based on this boxplot, write down the 5 number summary (you might have to estimate one or more of the
values).
(b) Estimate the interquartile range.
(c) Suppose that the boxplot provides an accurate representation of the salaries of the company’s 40,000
employees. Approximately how many of the 40,000 employees have salaries exceeding $60,000?
3. (old9) It is usual in finance to describe the returns from investing in a single stock by regressing the stock’s returns against
the market as a whole. This helps us see how closely a stock follows the general market. Data for Phillip Morris ( y) vs. S and
P 500 Index (x), July 1990 to May 1997 gave the mean of the x values, xbar = 1.304, the mean y of the values, ybar = 1.878,,
sx= 3.392, sy = 7.554,
r = .5251. A scatter plot showed no very influential observations.
(a) Find the least squares line for predicting Phillip Morris return from market return.
(b) Comment briefly on the “fit” of the Phillip Morris line.
4. The hourly wages of construction workers in different states in the USA are different. Here is a sample
of 8 hourly wages for eight states.
27, 25, 20, 15, 30, 34, 28, and 25.
(a) Create a Box-plot for these wages.
(b) Are there any outliers in this sample. Why or Why not?
(c) Is the distribution symmetric? If yes, why? If no, to which direction is it skewed?
(d) Compute the standard deviation of these hourly wages.
5. Here are 16 household incomes ( in thousand dollars) for a mid-size city in Ontario.
70
76
72
75
75
68
64
65
58
57
83
78
80
85
82
72
(a) Construct a stem plot for these data.
(b) What is the advantage of using the stem plot compared to the histogram?
6. To find the relation between the number of hours spent on studying BUEC232 per week and the final
score, a sample of 6 students were selected from a BUEC232 class in Fall, 200X and the following data
were obtained.
Student
#
1
2
3
4
5
6
Hours/week
3
5
6
8
12
16
final
score
35
65
72
75
85
96
The following numbers are also computed by Excel.
The average of “hours spent per week” is 8.333,
The standard deviation of “hours spent per week” is 4.844,
The average of “final scores” is 71.333,
The standard deviation of “final scores” is 20.829
(a) Compute the correlation coefficient. Is the relationship between these two variables strong?
(b) Develop a regression line for predicting the final score from the number of hours spent per week.
If a student spends 10 hours per week, what is this student’s predicted final score?
(c) Do you think that this regression line is reliable for predicting the final scores of BUEC students?
Why or why not?
Q7: True/False Questions. If you choose “False”, explain briefly.
1.For a data set with a highly skewed distribution, using mean and standard deviation is more appropriate than using
five number summary.
2. The inter-quartile range is used as a measure of variability to overcome the difficulty that the range is influenced too
much by extreme values.
3. .During a cold winter, the temperature stayed below zero for ten days (ranging from -20 to -5). The variance of the
temperatures of the ten day period is negative since all the numbers are negative.
4. If the correlation between two variables is close to zero, it means that there is no relationship between these two
variables.
5. Bar chart and the histogram show the same information.
6. Stem-plot and the histogram show the same information.
Q8. The household incomes of City A follow a normal curve with mean = 50k and standard deviation of 10k. The
household incomes of City B also follow a normal curve with mean = 70k and standard deviation of 15k. If the
middle income is defined as from 60k and 65k, which city has the higher proportion of middle income families?
Q9. (old8) A professor at a local university noted that the grades of her students were normally distributed with a mean of 78
and a standard deviation of 10.
a. What is the proportion of students who receive grades between 80 and 85?
b. The professor has informed us that 16.6 percent of her students received grades of A.
What is the minimum score needed to receive a grade of A? If 12.1 percent of her
students failed the course and received F's, what was the maximum score among
those who received an F?