Statistics- Your assignment should be submitted electronically
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 of study |
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.
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Rating:
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Solution: Statistics- Your assignment should be submitted electronically