Qab 105 Quantitative Analysis For Assessment Answers
Quantra Ltd. is a national wholesaler who provides a range of branded products to retailers with a recommended retail price for each product. The company has become aware that many retailers are selling products below the recommended price. In a random sample of 200 retailers, it was found that 79 retailers sold products below the minimum price. In order to assist the accountant with the report, you are asked to:
(a) Describe what a random sample is and how one can be selected.
(b) Calculate 95% confidence limits for the proportion of retailers selling below the recommended price and explain what this means.
Consider a random variables X with the following probability distribution:
X -4 0 1 2
P(x) 0.2 0.3 0.4 0.1
- P(x>0)
- P(x
- P(x≤ X ≤ 1)
- P(x = -2)
- P(x = -4)
- P(x < 2)
Homes in Blacktown city have a mean value of $88950. It is assumed that homes in vicinity of the city have a higher value. To test this theory, a random sample of 12 homes is chosen from the city area. Their mean valuation is $92460 and standard deviation is $5200. Complete a hypothesis test using α = 0.05. Assume prices are normally distributed.
Solve using p-value approach by using five steps model. A management accountant is attempting to derive a cost-output relationship for his company. The following data has been collected over the past two years.
|
Quarter |
Units of Output (000’) |
Cost $ 000’ |
|
1 |
10 |
32 |
|
2 |
20 |
39 |
|
3 |
40 |
58 |
|
4 |
25 |
44 |
|
1 |
30 |
52 |
|
2 |
40 |
61 |
|
3 |
50 |
70 |
|
4 |
45 |
64 |
(a) Using linear regression analysis, derive the relationship between the variables and interpret your answer.
(b) Estimate the strength of the relationship between the variables and explain the principle of the correlation co-efficient.
Answer:
Number of retailers sold products below the minimum price = 79
- A random sample is a population subset where every element has an equal chance or probability of being selected. A random sample can be selected by ensuring that all the retailers be given a unique number and then 200 numbers can be randomly selected from the whole population of numbers through software to avoid any bias. The retailers corresponding to the number selected would serve as part of the random sample (Hillier, 2006).
- 95% confidence limits for the proportion
Mean
Z value for 95% confidence interval = 1.96
95% confidence interval [0.327 0.4627]
Probability distribution
|
X |
-4 |
0 |
1 |
2 |
|
P(x) |
0.2 |
0.3 |
0.4 |
0.1 |
Mean value = $88950
Sample size n = 12
Mean valuation = $92460
Standard deviation s = $5200
Significance level
Prices are normally distribution.
Degree of freedom = n-1 = 12 -1 = 11
For t statistics = 2.338 and degree of freedom = 11, the p value (one tailed test) is computed as 0.0196.It is apparent that p value is lower than significance level (0.0196 <0.05). Hence, null hypothesis would be rejected and alternative hypothesis would be accepted (Flick, 2015). Therefore, it would be fair to conclude that mean prices of the Homes in Blacktown city is higher than $88,950.
Linear regression analysis
Dependent variable = Cost ($000’)
Independent variable = Units if Output (000’)
Interpretation
- Intercept = 21.25
It represents the cost when the unit of outputs produced is zero.
- Slope coefficient = 0.9615
It represents that when there is one unit increase in the unit outputs then the cost would be increased by a factor of 0.9615 (Hastie, Tibshirani and Friedman, 2011).
- Strength of relationship between costs and units of outputs
Correlation coefficient would be determined with the help of CORREL function.
Based on the above scatterplot and the correlation coefficient, it is apparent that there is a strong positive association between the given variables. The positive association is reflected from the positive slope of the scatter plot and the sign of the correlation coefficient. The magnitude of the correlation coefficient reflects the intensity of linear relationship (Hair et. al., 2015).
References
Flick, U. (2015). Introducing research methodology: A beginner's guide to doing a research project, 4th ed., New York: Sage Publications.
Hair, J. F., Wolfinbarger, M., Money, A. H., Samouel, P., and Page, M. J. (2015). Essentials of business research methods, 2nd ed., New York: Routledge.
Hastie, T., Tibshirani, R. and Friedman, J. (2011). The Elements of Statistical Learning, 4th ed., New York: Springer Publications.
Hillier, F. (2006), Introduction to Operations Research, 6th ed., New York: McGraw Hill Publications.
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