Population variance, Applied Statistics

Examining the Population Variance

Business decision making does not limit itself to setting up the hypothesis to test for the equality of more than two means or proportions simultaneously. This may be attributed to the everchanging and dynamic economic environment. It throws up situations wherein, the managers not only have to deal with the means and proportions but also have to objectively look at and probe the extent as well as the magnitude of the variability present in the population, determine the accuracy of the estimate and the degree of uncertainty that can be associated with such estimates.

In this part of the chapter, first we will look at the distribution of the sample variance for a population and conclude this chapter after looking at the distribution for the sample variance of two populations.

Inference about a Population Variance

Since it is difficult to collect information about the population in an exhaustive manner, we employ the sample variance (s2) as an estimate for the population variance (s2). The square root of s2 and s2 gives us the standard deviation of the sample and the population. But to calculate the limits, we require a sampling distribution. If the population variance s2, exhibits the characteristics of a normal distribution then the corresponding statistic is better described by a Chi Square distribution with n - 1 degrees of freedom. The Chi Square statistic for a sample variance is given by

              495_population variance.png  ......(1)

It is then possible to use Chi Square distribution to arrive at the confidence intervals for the parameter s2. Since the confidence intervals and the testing of the hypothesis is about s2 the population variance, equation (1) can be rewritten as   

951_population variance1.png

This facilitates us to find the confidence intervals for s2. The lower and the upper confidence intervals are given by

1580_population variance2.png

 

1514_population variance3.png

Figure

39_population variance4.png

Since we know the values of 1565_population variance5.png  , the square root of these two will give us the confidence interval for the standard deviation.

Posted Date: 9/15/2012 6:26:34 AM | Location : United States







Related Discussions:- Population variance, Assignment Help, Ask Question on Population variance, Get Answer, Expert's Help, Population variance Discussions

Write discussion on Population variance
Your posts are moderated
Related Questions
Circles or Pie Diagram: Circles or pie diagrams are alternative to squares. These are used  for the same purpose i.e. when  the values are differing  widely in their magnitude

the sum of mean and variance ofabinomia distribution of 5 trials is 9/5, find the binomial distribution.

Types of cost-reimbursable contracts are:   Cost Plus Fixed Fee contract (CPPF): Compensation is based on a fixed sum independent of the final project cost. The customer a

MARKS IN LAW :10 11 10 11 11 14 12 12 13 10 MARKS IN STATISTICS :20 21 22 21 23 23 22 21 24 23 MARKS IN LAW:13 12 11 12 10 14 14 12 13 10 MARKS IN STATISTICS:24 23 22 23 22 22 24 2

You are a business analyst working for a company called Combined Computers Pty Ltd. You have been asked to prepare a business report with statistics in it for the managing director

There are two types of drivers, high-risk drivers with an accident probability of 2=3 and low risk drivers with an accident probability of 1=3. In case of an accident the driver su

The box plot displays the diversity of data for the income; the data ranges from 20 being the minimum value and 1110 being the maximum value. The box plot is positively skewed at 4

Your company has developed a new product .Your company is a reputed company with 50% market share of same range of products. Your competitors also come with their new products equa

b. A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y

The regression line should be drawn on the scatter diagram in such a way that when the squared values of the vertical distance from each plotted point to the line are added, the to