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Business Statistics

Homework 1 (110 pts)

Remember, all work should be your own. Please submit your homework through

Cybercampus, by the beginning of class on 4/7. Late submission will be penalized. For all

graph questions, use computer softwares (excel etc) to produce them.

Problem 1 (10 points)

The following data represent the daily supply (y in thousands of units) and the unit price (x in

dollars) for a product.

Daily Supply (y) Unit Price (x)

5 2

7 4

9 8

12 5

10 7

13 8

16 16

16 6

a. Compute and interpret the sample covariance for the above data.

b. Compute the standard deviation for the daily supply.

c. Compute the standard deviation for the unit price.

d. Compute and interpret the sample correlation coefficient.

Problem 2 (10 points)

Global Engineers hired the following number of Class 1 engineers during the first six months of the

past year. (Assume the data represent a sample.)

Month No. of Class 1

Engineers Hired

January 3

February 2

March 4

April 2

May 6

June 0

a. Determine the mean, the median, the mode, and the range for the above data.

b. Compute the variance and the standard deviation.

c. Compute the z-scores for the months of May and June.

Problem 3 (10 points)

In a statistics class, the average grade on the final examination was 70 with a standard deviation of

10.

a. At least what percentage of the students received grades between 50 and 90?

b. Determine an interval for the grades that will be true for at least 80% of the students.

Problem 4 (5 points)

The variance of a sample was reported to be 144. The report indicated that ∑(𝑥 − �̅�)2 = 7200. What

has been the sample size?

Problem 5 (5 points)

The standard deviation of a sample was reported to be 20. The report indicated that ∑(𝑥 − �̅�)2 =

7200. What has been the sample size?

Problem 6 (10 points)

The following data shows the yearly income distribution of a sample of 200 employees at MNM,

Inc.

Yearly Income

(In $1,000s)

Number

of Employees

20 – 24 2

25 – 29 48

30 – 34 60

35 – 39 80

40 – 44 10

a. What percentage of employees has yearly incomes of $35,000 or more?

b. Is the figure (percentage) that you computed in Part a an example of statistical inference? If no,

what kind of statistics does it represent?

c. Based on this sample, the president of the company said that "45% of all our employees' yearly

incomes are $35,000 or more." The president's statement represents what kind of statistics?

d. With the statement made in Part c, can we be assured that more than 45% of all employees'

yearly incomes are at least $35,000? Explain.

e. What percentage of employees of the sample has yearly incomes of $29,000 or less?

Problem 7 (15 points)

A survey of 400 college seniors resulted in the following cross-tabulation regarding their

undergraduate major and whether or not they plan to go to graduate school.

Graduate School Undergraduate Major

Total Business Engineering Others

Yes 35 42 63 140

No 91 104 65 260

Total 126 146 128 400

a. Are a majority of the seniors in the survey planning to attend graduate school?

b. Which discipline constitutes the majority of the individuals in the survey?

c. Compute row percentages and comment on the relationship between the students'

undergraduate major and their intention of attending graduate school.

d. Compute the column percentages and comment on the relationship between the students'

intention of going to graduate school and their undergraduate major.

Problem 8 (10 points)

The following information regarding a sample of seven students is provided.

Student Identificatio

n number

Grade Point

Average

Classification Gender Rank in

Class

Adam 1234 2.89 Senior Male 15

Brandon 8978 2.01 Junior Male 25

Jason 6578 3.97 Freshman Male 2

Marissa 2345 3.98 Sophomore Female 1

Michelle 8901 2.67 Senior Female 18

Paula 7789 2.94 Senior Female 12

Webster 6780 3.77 Freshman Male 3

a. How many variables are in this data set?

b. How many observations are in this data set?

c. Which variables are qualitative and which are quantitative variables?

Problem 9 (10 Points)

The grade point average of the students at Sogang University is 2.80 with a standard deviation of

0.84. The grade point average of students at Yonsei University is 2.4 with a standard deviation of

0.84. Which university shows a more dispersed grade distribution? Explain your reasoning with

statistical evidence!

Problem 10 (25 points)

Consider the dataset “Retail.xlsx” (posted on Cybercampus under Homework 1, the first column

indicates the date and the second one is the US retail sales on that particular date). You can use

excel functions for these questions.

a. Calculate the relevant descriptive statistics for the monthly US retail sales variable (mean,

median, standard deviation, variance, min, max and range). Note: this is a sample.

b. Obtain the distribution (in other words, the histogram) for the monthly US retail sales

variable. By simply looking at the distribution what can you tell about the data set itself?

{Hint:} in order to obtain a histogram, you might want to make a frequency table first by

picking a reasonable number of ``bins''.

c. Obtain the time series graph (line graph of sales vs time) for the US retail sales. What do

you observe?