Assignment 1
Your assignment should be submitted
electronically. If you have problems writing formulas with your word processor,
cite the formula number as it appears in textbook. Show your work!Part marks are awarded only when detailed solutions are presented. If
only the answers are given, you will not receive any marks for incorrect
answers. You should submit solutions showing main calculations (i.e.,
procedures, formulas, and conclusions) for each and every problem.
Occasionally, an answer is wrong due to an arithmetic and/or computation error,
yet you could still get part marks if the formulas and procedures are correct.
Note:
You can use the Insert/Equation function to add
complex math to a Microsoft Word document. Be aware, though, that adding equations
increases the size of your files.
Question 1 (4
marks)
A medical journal reported the following frequencies of deaths due to
cardiac arrest for each day of the week.
Cardiac
Deaths by Day of the Week
Day f
Monday 40
Tuesday 17
Wednesday 16
Thursday 29
Friday 15
Saturday 20
Sunday 17
We want to determine whether the number of
deaths is uniform over the week.
a. Compute the
test statistic.
b. Using
the p-value approach at 95% confidence, test for the uniformity of death
over the week.
c. Using
the critical value approach, perform the test for uniformity.
Question 2 (4
marks)
The following table shows the results of recent study
regarding gender of individuals and their selected field of study.
|
Field |
Male |
Female |
TOTAL |
|
Medicine |
80 |
40 |
120 |
|
Business |
60 |
20 |
80 |
|
Engineering |
160 |
40 |
200 |
|
TOTAL |
300 |
100 |
400 |
We want to determine if the selected
field of study is independent of gender.
a. Compute the
test statistic.
b. Using
the p-value approach at 90% confidence, test to see if the field of
study is independent of gender.
c. Using
the critical method approach at 90% confidence, test for the independence of
major and gender.
Question 3 (3
marks)
The test scores for selected samples of sociology students who took
the course from three different instructors are shown below.
Instructor
A Instructor B Instructor C
83 90 85
60 55 90
80 84 90
85 91 95
71 85 80
Ata
= 0.05, test to see if there is a significant difference among the averages of
the three groups.
Question 4 (3
marks)
In
a completely randomized experimental design, 11 experimental units were used
for each of the 3 treatments. Part of
the ANOVA table is shown below.
Source of Sum Degrees Mean
Variation of Squares of Freedom Squares F
Between
Treatments 1,500 2? 750? 1.33?
Within
Treatments 4500? 8? 562.5?
(Error)
Total 6,000
a. Fill in the blanks in the above ANOVA table.
b. At 95% confidence, test to determine whether
or not the means of the 3 populations are equal.
1-0.95= 0.05/2= 0.025
Question 5 (6
marks)
A
factorial experiment involving 2 levels of factor A and 2 levels of factor B
resulted in the following.
Factor
B
Level
1 Level
2
Level
1 14 18
16 12
Factor A
Level
2 18 16
20 14
Set up an ANOVA table and test for any
significant main effect and any interaction effect. Usea
= .05.
Question 6 (10
marks)
A multiple regression analysis between yearly
income (Y in $1,000s), college grade point average (X1), age of the
individuals (X2), and the gender of the individual (X3;
zero representing female and one representing male) was performed on a sample
of 10 people, and the following results were obtained.
Coefficient Standard Error
Constant 4.0928 1.4400
X1 10.0230 1.6512
X2 0.1020 0.1225
X3 -4.4811 1.4400
Analysis of Variance
Source of Degrees Sum of Mean
Variation of
Freedom Squares Square F
Regression 360.59
Error 23.91
a. Write the
regression equation for the above.
b. Interpret the
meaning of the coefficient of X3.
c. Compute the
coefficient of determination.
d. Is the
coefficient of X1 significant?
Usea = 0.05.
e. Is the
coefficient of X2 significant?
Usea = 0.05.
f. Is the
coefficient of X3 significant?
Usea = 0.05.
g. Perform an F
test and determine whether or not the model is significant.
