An Introduction to Student's t-Distribution...

We know that we use the central limit theorem and the normal distribution to calculate probabilities where we assume that standard deviation for the population is given. This might be an ideal case as we might not have access to this value in practical situations.

Here is the point where t-distribution steps in. What we do is that we try to predict the population on the basis of sample drawn from it. And use its standard deviation for the actual population.

The equation that governs the process is:

$$T=\frac{\bar{x}-\mu }{s\sqrt{n}}$$

Example:

A chemical engineer clains that the population mean yield of a certain batch process is 500 gm/cu meter of the raw material. To check the claim he samples 25 batches each month. If the computed t-value falls between $\pm t_{0.005}$ then he is satisfied with the claim. What concentration should he draw from a sample that has mean of $\bar{x}=518$ and s=40 gm.

Manual Solution:

Form the table of t-distribution, $\pm t_{0.005}=1.711$ for n = 24 degrees of freedom. The probability is:

$$t=\frac{518-510 }{40\sqrt{25}}=2.18$$

when we look at the value of 2.25 in the body of the t-table under n=24 we found that it has chances of 0.02.

(to be continued...)

Using Excel To Solve System of Equations..

In Today's Post I will share with you a simple function that can be of tremendous help to you if you want to solve System of 3 Linear Equation. Such a System of Linear Equation is often represented like below: 

It might not be difficult to solve this if you have any high-end calculator for Texas or Casio or HP but in case you don't have one, you can use this sheet that i have setup. Here is a glance of how does this work:

Here i have added the co-efficient and the constant of the equation that facilitate the working of the excel function MDETERM(), since the function does not accept discontinuous ranges, we have to accommodate the sheet to overcome this hurdle. 

I am not going to add the manual workout of the problem but a snap shot of how this file save time:

you can see all done by just entering the data in few cells, rest is up-to the built-in function of excel 2007. Download this sheet and play with it..

A Premier of Process Costing based on Excel 2007

Well this is not an usual post based on some statistical functions, rather here i will discuss how to setup a Process Costing Sheet for yourself. If you have been employed as a Cost Accountant and you are just beginning your career, you might find a temple helpful in your work that can easily calculate the Process Cost. So here we go:

Steps: 

1. Setup a Sheet: 

Setup an Excel Sheet, with usual heading. These included Quantity Schedule, Cost Charged to the Department & Cost Accounted for by the Department. 

2. Develop Relations among Variables:

Yes, you need to develop the relations between the Variables. In Quantity Schedule we will be equating the Total Quantity Received against Quantity Transferred to the Next Department, Material Losses & Work In Process Inventory. You may Also want to add the Abnormal Losses in the sheet.

We also be calculating the Adjusted Amount of Finished Goods that is transferred to the next Department in order to account for the Work In Process Inventory.

The Example Question:

For December, the Production Control Department of Carola Chemical, reported the following data from Department 02:

Transferd in From Department 1........................... 55000 Liters
Tranfered out from Department 2......................... 39500 Liters
Work in Process Units (1/3rd Complete by Conv)........ 10500 Liters

All materials were put into process in Department 1

Unit Cost from Department 01 ............................ $ 1.8
Labour Cost in Department 02 ............................ 25720
Appalied Factory Overhead Department 02 ..............15480

Required: A Cost of Production Report for Department 02.

Solution:

Here is what is given you will need to do to get the solution:

The Solution is not possible without having some side-line calculation, the other part of the spread sheet will provide these values, see the following picture.

I have upload the Sample file here so that you can try it yourself. Hope that you will find it useful. Please provide your feedback. Thank you!!