Question 1 (7 marks)
Briefly discuss the following with relevant examples.
Population Parameter vs Sample Statistic
Descriptive Statistics vs Inferential Statistics
scales of measurement and importance of them in research
ANSWER: ** Answer box will enlarge as you type
Question 2 (7 marks)
BB research is a not-for-profit organization in Australia. They seek your help to decide the sampling plan one would choose to collect data for following research. In each case, you are required to explain (a) minimum of two alternative sampling methods, (b) importance of each method for the research and (c) process of sampling with hypothetical data on population and sample.
Government wants to analysis the peoples’ desire for covid vaccination and willingness to help for government plan for Covid free Australia
A group of researchers wants to estimate the living standard of people in regional Victoria.
(4 marks)
ANSWER:
The following table shows the monthly adverting expenditure and sales revenue of a company. You are required to estimate the covariance and correlation coefficient and explain what do these statistics tell you about the relationship between two variables and advice the company.
Sales revenue ($M) 9.6 11.3 12.5 9.5 8.5 12 11.4 12.5 13.8 14.6
Advertising expenditure ($000) 23 40 55 54 28 25 31 36 88 90
(3 marks)
(Note: Excel calculations are not allowed, and students are required to show all the steps in calculations)
ANSWER:
Question 3 (11 marks)
Sales team of a New Ventures Company is in the process of introducing a new product. As an initial step company conducted a survey of prospective customers. Estimate how large a sample should company take if they want to estimate the proportion of people who will buy the product to within 3%, with 99% confidence.
(3 marks)
ANSWER:
A researcher has taken a random sample of 8 observation from a normal population. Sample mean and standard deviations are 75 and 50 respectively. Using the 6 steps process of hypothesis testing.
Can he infer at the 10% significance level that the population mean is less than 100?
(3 marks)
ANSWER:
Can he infer at the 10% significance level that the population mean is less than 100 if population standard deviation is 50? (3 marks)
ANSWER:
Review the answers in (i) and (ii) and explain why the test statistics differed.
(2 marks)
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Question 4 (11 marks)
You have been given following data set related to sales of Product X(units) in 3 different locations.
Location 1 45 27 39 42 28
Location 2 30 29 36 21 24
Location 3 19 25.5 27.6 31.5 34.6
You are required to answer following questions.
State the null and alternative hypothesis for single factor ANOVA to test for any significant difference in sales in three locations. (1 marks)
ANSWER:
State the decision rule at 5% significance level. (2 marks)
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Calculate the test statistic. (6 marks)
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Based on the calculated test statistics, decide whether there are any significant differences between the sales. (2 marks)
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Note: No excel ANOVA output allowed. Students need to show all the steps in calculations.
Question 5 (7 marks)
An agronomist undertook an experiment to investigate the factors that potato harvest. In his research, agronomist decided to divide the farm into 30 half hectare plots and apply varies level of fertilizer. Potato was then planted and the harvest at the end of the season was recorded.
Fertilizer(Kg) Harvest (tons)
210 43.5
220 40.0
230 48.0
240 65.0
250 80.0
260 85.0
270 95.0
280 80.0
290 97.3
Note: No excel ANOVA output allowed. Students need to show all the steps in calculations.
You are required to;
Find the simple regression line and interpret the coefficients. (3 marks)
ANSWER:
Find the coefficient of determination and interpret its value. (2 marks)
ANSWER:
Does the model appear to be a useful tool in predicting the potato harvest? If so, predict the harvest when 250KG of fertilizer is applied. If not explain why not. (2 marks)
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Question 6 (7 marks)
ABX Delivery provides the service across all the states in Australia. Marketing manager of this company wants to identify key factors that affect the time to unload a truck. A random sample of 50 deliveries was observed following data were reported.
Time to unload a truck (in minutes),
total number of cartons and
the total weight (in hundreds of Kilograms).
Following tables shows the regression output of the sample data set.
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.836420803
R Square 0.699599759
Adjusted R Square 0.68681677
Standard Error 8.823384264
Observations 50
ANOVA
df SS MS F Significance F
Regression 2 8521.530836 4260.765 54.72897 0.000000
Residual 47 3659.049164 77.85211
Total 49 12180.58
Coefficients Standard Error t Stat P-value
Intercept -13.669 7.829028389 -1.74599 0.087346
Cartons 0.5172 0.067246763 7.691119 0.000000
Weight 0.2901 0.11166803 2.597671 0.012494
Determine the multiple regression equation (1 mark)
ANSWER:
Develop hypothesis and assess the independent variables significance at 5% level?
(2 marks)
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How well does the model fit the data? (2 marks)
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Propose minimum of 2 new explanatory variables to the model and discuss the implication of OLS assumptions in regression analysis. (2 marks)
ANSWER:
END OF FINAL ASSESSMENT
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