Question 1
a) Random sampling is a method of sampling in which each member of a population has equal chances of being included into the sample. Each member of the sample is chosen entirely by chance.
Since each member has equal chances, one advantage of the random sampling method is that it is fair and unbiased. The random sample chosen can properly represent the population it is taken from. One disadvantage of random sampling is that there is no systematic approach in choosing the sample. If the population being studied becomes larger, the fairness of the random sampling method becomes more difficult to maintain.
b) The definitions from of primary and secondary data are the following:
“primary data – Original data collected for a specific research goal.
secondary data – Data originally collected for a different purpose and reused for another research question.”
Based on these definitions, the given data are primary data from company’s point of view. The reason is because the data were gathered by the company’s management for a particular purpose – to analyse the extent to which price is able to predict sales. The problem details do not mention of the previous use for the data, thus it can be assumed in this assignment that the original research goal for the data is for analysing the extent to which price is able to predict sales.
c) It is observed that the sales value in the year 2013 is an outlier (Sales = 6509). This value is almost twice the magnitude of the other sales values for the other years. All the other sales values are in the £3000+ range; the sales value in the year 2013 is the only one outside this range. There are no observed outliers for the price values.
d) i) ii)
The two measures of averages are the mean and the median. The three measures of spread are the range, the standard deviation, and the variance. The excel results are displayed in the following table:
The median is computed using MEDIAN function. The mean is computed using the AVERAGE function. The range is computed by subtracting the minimum value from the maximum value; the minimum value is acquired using the MIN function, while the maximum value is acquired using the MAX function. The standard deviation is computed using the STDEV.S function, and the variance is computed using the VAR.S function.
The prices data included in the computation are from years 2002 to 2013. The sales data included in the computation are from years 2002 to 2012 (excluding the outlier in 2013).
e) i) ii)
The scattered diagram of the sales versus the prices is:
iii) The y-intercept of the regression line is Sales = 5698.2, and the slope of the regression line is -118.88.
iv) The slope of the regression line is negative. This means that as the prices increase, the sales will in turn decrease. More accurately, for every £1 increase in the price from year-to-year, there is approximately 119 decrease in the total sales in the present year.
v) The intercept of the regression line indicates the value of sales when the price reaches zero. This is only theoretical because practically speaking the company will not make any sales if the price is zero. Thus, this intercept value makes no sense in practice. However, this can be used as theoretical maximum value of sales. In this sense, the company may use this information to judge (whether it is high or low) the sales value it achieves in a year.
f) A £2 price increase would theoretically cause a 2×118.88=237.76≈238 decrease in sales.
g) In 2014, the average price is £25. The expected sales value in this year is:
Y=-118.88X+5698.2=-118.8825+5698.2=2726
h) The linear model is not appropriate for very large or very small price values. Just from visual observation of the regression line drawn alongside the data points, it can be concluded that the linear model does not accurately represent the behaviour of the data points. Moreover, the outlier observed in the year 2013 cannot be neglected in considering the integrity of the model. Also, the spread values of Y are quite large; this is even without the outlier. Therefore, the price values beyond these measurements could easily produce unpredictable sales results.
The regression analysis showed that there is an inverse relationship between the average price and the sales per year. This means that when the average price in a year is high, the total sales value for the present year is low. While this is a negative outcome, the opposite is also true—when the average price in a year decreases, the total sales for the present year increases. Thus, the sales of the company can effectively be controlled by setting the price appropriately.
There is no need for Tata Steel UK to close down operations. However, the operational expenses should be managed and controlled in such a way that the product price is not severely affected. By maintaining the price into low levels without sacrificing profit, the sales can dramatically increase. The data from 2012 to 2013, in which the average price did not change, showed an almost doubled increase in the sales. Some of the highest sales were also recorded in the years when the prices are lowest (year 2011, price 18.4, sales 3622) (year 2003, price 18.6, sales 3430). Thus, it is advised that the prices are maintained low.
This analysis shows that the labor sector of the company has no direct effect on the sales outcome of the company per year. Therefore, the jobs of the employees should not be compromised when it comes to deciding whether or not to continue the operations of Tata Steel UK. Adjustments can be made on several other factors like raw materials expenses, operational expenses, etc. in order to achieve a significantly low price value. By doing this, the sales of the company will soar, and there will be no need for closing down.
References
Easton, VJ & McColl, JH 1997, Random Sampling, viewed 17 May 2016, <http://www.stats.gla.ac.uk/steps/glossary/sampling.html#randsamp>.
Hox, JJ & Boeije, HR 2005, 'Data Collection, Primary vs. Secondary', in Encyclopedia of Social Measurement Volume 1, Elsevier Inc.
