Stats 101

Question 1

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. [3 Marks]

(b) Calculate 95% confidence limits for the proportion of retailers selling below the recommended price and explain what this means. [3 Marks]

Question 2

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

Find the following probabilities: [0.5 Mark each = 3 marks]

a. P(x>0)

b. P(x

c. P(x≤ X ≤ 1)

d. P(x = -2)

e. P(x = -4)

f. P(x < 2)

Question 4

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. [5 Marks]

Question 5

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.

Year	Quarter	Units of Output (000’)	Cost $ 000’
2010	1	10	32
	2	20	39
	3	40	58
	4	25	44
2011	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. [3 Marks]

(b) Estimate the strength of the relationship between the variables and explain the principle of the correlation co-efficient. [3 Marks]

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