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Binomial Distribution
The HR department reviewed its data over the past 10 years regarding employees that applied and from what schools they came from. It showed that 5% came from “Ivy League” universities. The average response rates for job ads are 10 per day.
Recently, the CEO announced a critical project that should start 2 weeks from now. He wanted to hire at least 3 “Ivy League” graduates as possible. His question is: What are the chances of getting 3 applications of these graduates in the next 2 weeks? Depending on the chances, he may move the project start at a later date.
For the binomial distribution, the success chance for each application is 5%. The maximum number of applications is 10 each for 10 days which makes 100. The number of desired applications is 3, at the least. By applying the binomial formula:
= 1- BINOMDIST(2,100,0.05,0)
the answer would be 88%.
The CEO decided to add 2 more weeks for 200 applications, which would give a higher 99.7%.
Normal Distribution
One variable in the workplace that can have a normal distribution is the travel time of employees going to the office. There can be actions that can be taken based on this data. One is where the optimum location of the office is so the overall travel time is reduced. Another is the possibility of giving travel subsidy to those who live the farthest. At the moment, the latter was chosen to be of most interest for the company and the limit set is at 85% or about one standard deviation from the mean. The following is the case in point.
EMPLOYEE TRAVEL TIME (MINS)
1 30
2 120
3 70
4 15
5 90
6 40
7 150
8 65
9 45
10 100
The mean is 72.5 and the standard deviation is 42.57 minutes. That figure offset from the mean would be 72.5 plus 42.57 which equals 115. From the table, all those above 115 minutes can get travel subsidy. They are Employees 2 and 7.
Confidence Interval for a Mean
In April of last year, the US Bureau of Labor Statistics reported that nonfarm payrolls grew by only 226,000, which varied from a survey by the Wall Street Journal by 102,000 which is a large 45%. This was to have been an indicator of a decrease in the unemployment rate by 5.5%. With such variance, people have been alluding to accusations of deliberate deception to show a better than expected jobs market situation.
Economists and statisticians though point to the size and complexity of the US economy that may show conflicting reports. Mention of the confidence interval should give a better perspective. In this case, the confidence interval of the nonfarm payrolls is 90%, given plus or minus 105,000. This then brings a range of 123,000 to 333,000 which covers the figures of the Bureau and the survey. (Spencer)
With the large spread, analysts were encouraged to look at other indicators such as the payrolls trend and the four-week rolling average of weekly jobless claims.
Correlation and Regression
The shape of the data is usually formed by the collection and pattern of dots representing instances. For correlation, what we are looking for is how well the shape of the data is forming a line. Just by looking at the shape of the data, one can see the ‘strength’ of the line being formed. Linear correlations are quantified as +/- 1 (perfect), +/- 0.9 (high), +/-0.5 (low) and 0 (none).
Regardless of the strength of the correlation (formation of the line) and if it is no-zero, it is either positive or negative. It is positive if the line appears to be rising from left to right or negative if it appears to be falling from left to right.
One indicator if there is a line that can be formed is the presence of two end dots that can be the ends of the line. There should only be one such pair. If there can be another pair, then it shows that the data has no correlation at all. It would look like a block or round mass of dots.
Linear Correlations and Regression Analysis
Both tests may use the same set of data or data shape and the ensuing line that can be formed if it is possible. The task of linear correlation is to determine a the coefficient r which states the strength of the linear relationship of two variables. It is definitive of a current state. The task of regression is determine the equation of the line formed from the same data shape which would allow the prediction of the value of a dependent variable based on the value of an independent variable. Regression is predictive of a future state.
A question that can be answered by a correlation can be: “For the past 5 years, how much did the volume of sales decrease for every dollar increase in price?”. For the same case, a question for regression can be formed: “If we will use the sales data of the last 5 years, what will be the volume of sales if we increase our price by 10%?”
Works Cited
Spencer, Jakab. "Don’t Check the Jobs Number; Check the Trend". Wall Street Journal, 7 May 2015. Web. 9 March 2016. <http://www.wsj.com/articles/dont-check-the-jobs-number-check-the-trend-1431018278>.
