Reference no: EM132576851
HI6007 Statistics for Business Decisions Assessment Task - Tutorial Questions, Holmes Institute, Australia
Purpose - This assignment is designed to assess your level of knowledge of the key topics covered in this unit.
Unit Learning Outcomes Assessed:
1. Students are able to apply appropriate business research methodologies to support decision-making process.
2. Students are able to identify and apply valid statistical techniques in a given scenario to solve business problems.
3. Students are able to justify and interpret the results of a statistical analysis in the context of critical reasoning for a business problem solving.
4. Students are able to apply statistical knowledge to summarize data graphically and statistically, either manually or via a computer package.
5. Students are able to justify and interpret statistical/analytical scenarios that best fit business solution.
6. Students are able to justify value and limitations of the statistical techniques to business decision making.
Questions -
Question 1 - A local health centre noted that in a sample of 400 patients, 80 were referred to them by the local hospital.
a. Provide a 95% confidence interval for all the patients who are referred to the health centre by the hospital.
b. What sample size would be required to estimate the proportion of all hospital referrals to the health centre with a margin of error of 0.04 or less at 95% confidence?
Question 2 - The average starting salary of students who graduated from colleges of Business in 2009 was $48,400. A sample of 100 graduates of 2010 showed an average starting salary of $50,000. Assume the standard deviation of the population is known to be $8000. We want to determine whether or not there has been a significant increase in the starting salaries.
Step 1. Statement of the hypothesis
Step 2. Standardised test statistic formula
Step 3. State the level of significance
Step 4. Decision Rule (Draw a bell to show rejection zone)
Step 5. Calculation of the statistic
Step 6. Conclusion
Question 3 - The data in the table below presents the hourly quantity of production for three lines of production processes over the first 4 days in XYZ Company. Answer the questions based on the Excel Output given below.
|
Day
|
Process 1
|
Process 2
|
Process 3
|
|
1
|
33
|
33
|
28
|
|
2
|
30
|
35
|
36
|
|
3
|
28
|
30
|
30
|
|
4
|
29
|
38
|
34
|
ANOVA: Single Factor
SUMMARY
|
Groups
|
Count
|
Sum
|
Average
|
Variance
|
|
Process 1
|
4
|
120
|
30
|
4.66667
|
|
Process 2
|
4
|
136
|
34
|
11.3333
|
|
Process 3
|
4
|
128
|
32
|
13.3333
|
ANOVA
|
Source of Variation
|
SS
|
df
|
MS
|
F
|
P value
|
|
Between Groups
|
32
|
?
|
?
|
?
|
|
|
Within Groups
|
88
|
?
|
?
|
|
|
|
Total
|
120
|
11
|
|
|
|
a. State the null and alternative hypothesis for single factor ANOVA.
b. State the decision rule (α = 0.05).
c. Calculate the test statistic.
d. Make a decision.
Question 5 - Personal wealth tends to increase with age as older individuals have had more opportunities to earn and invest than younger individuals. The following data were obtained from a random sample of eight individuals and records their total wealth (Y) and their current age (X).
|
Person
|
Total wealth ('000s of dollars) Y
|
Age (Years) X
|
|
A
|
280
|
36
|
|
B
|
450
|
72
|
|
C
|
250
|
48
|
|
D
|
320
|
51
|
|
E
|
470
|
80
|
|
F
|
250
|
40
|
|
G
|
330
|
55
|
|
H
|
430
|
72
|
A part of the output of a regression analysis of Y against X using Excel is given below:
SUMMARY OUTPUT
|
Regression Statistics
|
|
Multiple R
|
0.954704
|
|
R Square
|
0.91146
|
|
Adjusted R Square
|
0.896703
|
|
Standard Error
|
28.98954
|
|
Observations
|
8
|
ANOVA
|
|
df
|
SS
|
MS
|
F
|
Significance F
|
|
Regression
|
1
|
51907.64
|
51907.64
|
|
|
|
Residual
|
6
|
5042.361
|
840.3936
|
|
|
|
Total
|
7
|
56950
|
|
|
|
|
|
Coefficients
|
Standard Error
|
t Stat
|
P-value
|
|
Intercept
|
45.2159
|
39.8049
|
|
|
|
Age
|
5.3265
|
0.6777
|
|
|
a. State the estimated regression line and interpret the slope coefficient.
b. What is the estimated total personal wealth when a person is 50 years old?
c. What is the value of the coefficient of determination? Interpret it.
d. Test whether there is a significant relationship between wealth and age at the 10% significance level. Perform the test using the following six steps.
Step 1. Statement of the hypotheses
Step 2. Standardised test statistic
Step 3. Level of significance
Step 4. Decision Rule
Step 5. Calculation of test statistic
Step 6. Conclusion
Question 6 - A student used multiple regression analysis to study how family spending (y) is influenced by income (x1), family size (x2), and additionsto savings(x3). The variables y, x1, and x3 are measured in thousands of dollars. The following results were obtained.
|
ANOVA
|
|
|
|
|
df
|
SS
|
|
Regression
|
3
|
45.9634
|
|
Residual
|
11
|
2.6218
|
|
Total
|
|
|
|
|
Coefficients
|
Standard Error
|
|
Intercept
|
0.0136
|
|
|
x1
|
0.7992
|
0.074
|
|
x2
|
0.2280
|
0.190
|
|
x3
|
-0.5796
|
0.920
|
a. Write out the estimated regression equation for the relationship between the variables.
b. Compute coefficient of determination. What can you say about the strength of this relationship?
c. Carry out a test to determine whether y is significantly related to the independent variables. Use a 5% level of significance.
d. Carry out a test to see if x3 and y are significantly related. Use a 5% level of significance.