Statistics

MGMT 1501 F10 A1 TOTAL marks = 14 + 13 + 23 = 60

Name (print): __________________________ Mark:___________/60_____

Student #: __________________________

Tutorial Section: __________________________

Due Date: Mon. Sept 23, 2019

Time: 10:00 a.m.

Location: YOUR tutorial drop box

Notes:

1. Print out a hard copy of this assignment and then answer each question in the space

provided using pen or pencil. Hand in this hard copy with your answers written on it.

Ensure all the numbered pages are in the correct order. Failure to do so will result in a

grade of 0 for the assignment.

2. Please do not change the pagination.

3. Please show all rough work and not just the final answer.

4. Assignments are to be done individually. Plagiarism will not be tolerated.

5. Assignments are to be remitted to the appropriate drop box by the due date and time.

6. Late assignments will not be accepted.

7. Be sure to use correct notation and show how you find each answer. Include concluding

statements.

1. [14 marks ] The Datafile MedianHousehold contains the median household income for a family with

two earners for each of the fifty states (American Community survey, 2013).

a. [3 marks] By hand, construct a frequency, percent frequency and cumulative percent

frequency distribution of median household income. Begin the first class at 65.0 and use

a class width of 5.

Median Household Income ($1000s) Frequency % Frequency Cumulative %

Total

b. [3 marks] Construct a frequency histogram using Minitab. (Include as next page.)

TOTAL marks for page = [6]

c. [2 marks] Comment on the shape of the distribution.

d. [2 marks] Which state has the highest median income for two-earner households?

e. [2 marks] Which state has the lowest median income for two-earner households?

f. [2 marks] Construct a stem and leaf display using Minitab. (Insert as next page.)

TOTAL marks for page = [8]

2. [13 marks ] Fortune magazine’s list of the world’s most admired companies for 2014 is

provided in the data contained in the file AdmiredCompanies (Fortune, March 17, 2014). The

data in the column labelled Return shows the one-year total return (%) for the top ranked 50

companies. For the same time period, the S&P average return was 18.4%.

a. [2 marks]Compute the median return for the top ranked 50 companies.

b. [2 marks]What percentage of the top-ranked 50 companies had a one-year return greater

than the S&P average return?

c. [3 marks]Develop a five number summary for the data.

d. [2 marks]Are there any outliers? (State your criteria for “outliers”.)

TOTAL marks for page = [10]

e. [4 marks]Develop a box plot for the one-year total return, by hand.

TOTAL marks for page = [4]

3. [23 marks] The Access Video Games (AVG) operates a webserver, which provides a wide range of

free online video games. It is critical for AVG to maintain customer engagement and satisfaction,

which is measured by the monthly active hours of each account. The marketing director Garry Finley

is interested in whether the monthly active hours have increased after a new user interface was

implemented in August, 2015. As a first step in the analysis, Garry selected a random sample of 20

accounts in July, and another random sample of 20 accounts in September. The monthly active hours

are given below.

Before 25 32 42 29 28 35 42 28 25 29 �� = 666

38 26 40 34 32 38 30 40 44 29 ��� = 22,898

After 36 45 54 36 28 34 38 45 60 42 �� = 904

32 41 30 55 36 64 60 64 56 48 ��� = 43,464

Use the summary statistics provided (where appropriate ); show your hand calculations.

a) [6 – 1 mark each] Calculate the mean, median and mode for the monthly active time in the two samples.

TOTAL marks for page = [6]

b) [15] Calculate the range, inter-quartile range, the standard deviation, and the coefficient of variation

of the monthly active time for each of the samples. Complete the table.

Before After

Range [2]

Interquartile

Range

[5 – 1 mark

per quartile;

0.5 mark per

IQR]

Standard

Deviation[6]

Coefficient

of

variation[2]

TOTAL marks for page = [15]

c) [2] Using the results in (a) and (b), comment on the effectiveness of the new user interface.

Is the new user interface successful in increasing customer engagement? Explain briefly.

TOTAL marks for page = [2]