Question

QUESTION 4

State whether each of the following are TRUE or FALSE, and explain your reasoning for the answer:

1. The binomial distribution is defined by its mean and standard deviation.

2. As the sample size increases, the standard error of the mean decreases.

3. If the population distribution is unknown, in most cases the sampling distribution of the mean can be approximated by the normal distribution if the samples contain at least 10 observations.

(b)       Suppose the following trend line and seasonal indices were obtained from four (4) years of sales data (in $ million) for a multinational grocery chain from 2012 to 2015.

Trend line:        y_t = 112 + 2.6t

Seasonal Effect:

Quarter	1	2	3	4
Seasonal Index	0.8	1.1	0.9	1.2

1. Interpret fully the seasonal indices for the first and second quarters.

   (1 mark)

2. Forecast the sales value in the fourth quarter for the next year (2016).

(1 mark)

Answer 1

TRUE or FALSE: a) False, the binomial distribution is defined by n, the sample size, and p, the success probability.

b) False, the standard error of mean is given by . Thus the standard error is inversely proportional to the sample size. Hence as the sample size increases the standard error of the mean decreases.

c) False, the required sample size must be at least 30.

(b) i) Interpretation: Seasonal indices have an average value of 1. This can be converted into a percentage for easier interpretation. For example, a seasonal index of 0.8 (or 80%) for the first quarter indicates that that season had 20% fewer sales than the seasonal average. Similarly, a seasonal index of 1.1 (or 110%) for the second quarter indicates that that season had 10% more sales than the seasonal average.

ii) For the fourth quarter of 2016, t= 20 as t=1 for the first quarter of 2012, Using the trend line we get trend = 112+2.6*20=164, while the seasonal index is 1.2, thus forecast of the sales is 164*1.2 = 196.8