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.