Reference no: EM132798372

HI6007 Statistics for Business Decisions - Holmes Institute

Learning Outcome 1: Understand appropriate business research methodologies and how to apply them to support decision-making process.

Learning Outcome 2: Understand various qualitative and quantitative research methodologies and techniques.

Learning Outcome 3: Explain how statistical techniques can solve business problems;

Learning Outcome 4: Identify and evaluate valid statistical techniques in a given scenario to solve business problems;

Learning Outcome 5: Explain and justify the results of a statistical analysis in the context of critical reasoning for a business problem solving

Learning Outcome 6: Apply statistical knowledge to summarize data graphically and statistically, either manually or via a computer package;

Learning Outcome 7: Justify and interpret statistical/analytical scenarios that best fits business solution;

Learning Outcome 8: Explain and justify value and limitations of the statistical techniques to business decision making and;

Learning Outcome 9: Explain how statistical techniques can be used in research and trade publication

The questions to be answered are;

Question 1
a. With your own words, using relevant examples briefly define types of probability assigning methods
b. Transport trade association conducted a survey of their members to determine what they felt were the important issues to be discussed with the management. The survey results showed that 74% felt that the job security was the important issue, while 65% felt that salary increment was an important issue. Of those who felt salary increment was an important issue, 60% also felt that job security was an important issue.
i. What percentage of the members felt that both job security and salary increment were important?
ii. What percentage of the members felt that at least one of these two issues was important?

Question 2
Annual food consumption survey shows that number of instant food meals consumed per month by university students is normally distributed with a mean of 10 and a standard deviation of 3.
a. Calculate the proportion of students consume more than 12 instant meals per month?
b. Estimate the probability that in a random sample of 25 students' more than 275 instant meals are consumed.

Question 3
D Dax limited installed a new safety equipment in order to reduce the number of person hours lost as a result of industrial accident. In a test to of the effectiveness of the equipment, a random sample of 50 departments was chosen. The number of person- hours lost in the month prior to and the month after the installation of the safety equipment was recorded. The percentage change was calculated and recorded. Assume that the population standard deviation is 5 and sample mean is -1.2. Can we infer at the 10% significance level that the new safety equipment is effective?

You are required to
a. Formulate hypotheses
b. Decide the suitable test statistics and justify your selection.
c. Calculate the value of the relevant test statistics and identify the P value
d. Based on the test statistics in part (III), decide the decision criteria.
e. Make the final conclusion based on the analysis.

Question 4
The table below shows data on research to examine the perception of business ethics among 3 groups of employees (higher score indicates higher ethical values).

A	B	C
6	5	6
5	5	7
4	4	6
5	4	5
6	5	6
4	4	6
5	5	6
4	6	6
6	5	4
5	6	5

a. State the null and alternative hypothesis for single factor ANOVA to test for any significant difference in the perception among three groups.
b. State the decision rule at 5% significance level.
c. Calculate the test statistic.
d. Based on the calculated test statistics decide whether any significant difference in the mean price of gasoline for three bands.
Note: No excel ANOVA output allowed. Students need to show all the steps in calculations.

Question 5
Relax mortgage has gathered following data to examine the relationship between housing starts and mortgage interest rate.

Interest rate	3.5	3.0	2.8	3.6	2.75	3.4	3.12	2.86	3.02	2.6	3.3
Housing starts	100	120	150	130	170	135	130	185	127	190	96

You are required to;
i. Derive the regression equation
ii. Estimate the no of housing starts if mortgage interest rate is 2.5%
iii. Calculate and interpret the correlation between interest rate and no of housing starts.

Question 6
D& T LTD marketing team needed more information about the effectiveness of their 3 main mode of advertising. To determine which type is the most effective, the manager collected one week's data from 25 randomly selected stores. For each store, the following variables were recorded:
Weekly gross sales
Weekly expenditure on direct mailing (Direct)
Weekly expenditure on newspaper advertising (Newspaper) Weekly expenditure on television commercials (Television)
Following is the regression output based on the above-mentioned data.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.442
R Square	A
Adjusted R Square	0.080
Standard Error	2.587
Observations	25
ANOVA
	Df	SS	MS	F	Significance F
Regression	B	34.1036	E	F	0.1979
Residual	21	D	6.6933
Total	C	174.6631
	Coefficients	Standard Error	t Stat	P- value	Lower 95%
Intercept	12.31	4.70	2.62	0.02	2.54
Direct	0.57	1.72	H	0.74	-3.01
Newspaper	3.32	1.54	2.16	0.04	0.12
Television	G	1.96	0.37	0.71	-3.34

a. Complete the missing entries from A to H in this output
b. Assess the independent variables significance at 5% level
c. Does the model is significant at 5% level?

Attachment:- Statistics for Business Decisions.rar