Durga Auto Ltd is an auto spare parts manufacturing company in Jamshedpur . It was founded by two brothers Sumanta Chatterjee and Hemanta Chatterjee in 1982.

BACKGROUND
These two brothers completed their schooling till 11th & 12th Class respectively, and then dropped out from the formal education, because their parents wanted them to do something on their own instead of becoming a government employee.

EVOLUTION OF Durga Auto Ltd
They started a motor garage in 1977, then started their own spare part manufacturing unit for heavy vehicles in 1983.

CREATING TRUST : They started the business with just fourteen workers. It took them seven years to scale up, as gaining the trust of the customers was difficult. They were able to work with 60 workers, had Telco as their major customer and did a business of Rs 2 crore in 1990. As they gained confidence, they continuously scaled up and they even entered the car-auto segments by 2002.

The company had shown consistent performance till last year in the Indian market of Rs 6000-7000 crore . However in the last quarter of, the net profits and net sales dipped by 20 percent and 25 percent respectively.

The CFO of Durga Auto , Sumanta Chatterjee , directed the controller, Debashish Bose to present an account of the budgeted and actual performance of the company for the current month. Debashish with the help of Chief Account Accountant, Anand Singh presented the relevant cost/profit data summarised in Exhibit 1

Based on the above, the controller prepared a comparative profit statement to present to CFO. (Exhibit 2)

Question : Prepare a detailed variance analysis and highlight the remedial measures that Durga Auto should take to remedy the situation arising out of declining profitability and sales in recent months and fix responsibility for the variance.

...Analysis of Variance
Lecture 11 April 26th, 2011
A. Introduction
When you have more than two groups, a t-test (or the nonparametric equivalent) is no longer applicable. Instead, we use a technique called analysis of variance. This chapter covers analysis of variance designs with one or more independent variables, as well as more advanced topics such as interpreting significant interactions, and unbalanced designs.
B. One-Way Analysis of Variance
The method used today for comparisons of three or more groups is called analysis of variance (ANOVA). This method has the advantage of testing whether there are any differences between the groups with a single probability associated with the test. The hypothesis tested is that all groups have the same mean. Before we present an example, notice that there are several assumptions that should be met before an analysis of variance is used.
Essentially, we must have independence between groups (unless a repeated measures design is used); the sampling distributions of sample means must be normally distributed; and the groups should come from populations with equal variances (called homogeneity of variance).
Example:
15 Subjects in three treatment groups X,Y and Z.
X Y Z
700 480 500
850 460...

...BUDGET MANAGEMENT ANALYSIS
To have a basis in illustrating the analysis of variance or difference between budgeted and actual figures, the budget of a sampled (unknown) company was utilized (http://www.smallbusinessnotes.com/business-finances/budgeting-systems.html).
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...of the MANOVA, check outcomes that test other assumptions for this statistic: equality of covariance matrices (see Box's Test) and sufficient correlation among the DVs (see Bartlett's Test of Sphericity). Also check the results of the Levene's Test of Equality of Error Variances to evaluate that assumption for the univariate ANOVAs that are run and show in the Tests of Between-Subjects Effects output. What have you found about whether the data meet these additional assumptions for the MANOVA and follow-up ANOVAs? Explain.
HINTS:
Once in the Options box, remember to check box for "Residual SSCP matrix" to get results for the Bartlett's test.
Also, remember to ask for post hoc tests for Treatment because there are more than two conditions. Profile plots also help with visualizing interactions.
6. What are the outcomes of the multivariate tests (main effects and interaction)? Report either the Pillai's Trace or Wilks's Lambda for each result, as well as the associated F-value and its statistical significance. Use the following format for notation to report each result: Pillai's Trace OR Wilks' lambda = ____; F(df, df) = ____, p = ____.
HINTS:
Use Pillai's trace if there are problems with heterogeneity of variance-covariance matrices for the DVs. Otherwise, Wilks' lambda is fine.
Eta squared cannot be calculated from the information provided in the multivariate tests results.
7. Given the results of the multivariate tests, would you now move...

...INTRODUCTION TO ONE-WAY ANALYSIS OF VARIANCE
Dale Berger, Claremont Graduate University http://wise.cgu.edu
The purpose of this paper is to explain the logic and vocabulary of one-way analysis of variance (ANOVA). The null hypothesis tested by one-way ANOVA is that two or more population means are equal. The question is whether (H0) the population means may equal for all groups and that the observed differences in sample means are due to random sampling variation, or (Ha) the observed differences between sample means are due to actual differences in the population means.
The logic used in ANOVA to compare means of multiple groups is similar to that used with the t-test to compare means of two independent groups. When one-way ANOVA is applied to the special case of two groups, one-way ANOVA gives identical results as the t-test.
Not surprisingly, the assumptions needed for the t-test are also needed for ANOVA. We need to assume:
1) random, independent sampling from the k populations;
2) normal population distributions;
3) equal variances within the k populations.
Assumption 1 is crucial for any inferential statistic. As with the t-test, Assumptions 2 and 3 can be relaxed when large samples are used, and Assumption 3 can be relaxed when the sample sizes are roughly the same for each group even for small samples. (If there are extreme outliers or errors in...

... 2/21/2014
274 EXERCISE 36 • Analysis of Variance (ANOVA) I
1. The researchers found a significant difference between the two groups (control and treatment) for change
in mobility of the women with osteoarthritis (OA) over 12 weeks with the results of F(1, 22) 9.619,
p 0.005. Discuss each aspect of these results. F is the statistic for ANOVA. F (1,22) one represents the number of groups in the study and 22 equals the subjects used the error df, and 9.619 is significant as it is P=0.005, it can be said that the intervention group participants face a significant reduction in mobility difficulty.
2. State the null hypothesis for the Baird and Sands (2004) study that focuses on the effect of the GI with
PMR treatment on patients’ mobility level. Should the null hypothesis be rejected for the difference between
the two groups in change in mobility scores over 12 weeks? Provide a rationale for your answer.
Ho 1: Guided imagery (GI) with Progressive Muscle Relaxation reduces pain difficulties of women with OA.
Ho 2: Guided imagery (GI) with Progressive Muscle Relaxation reduces mobility difficulties of women with OA.
The null hypothesis should be accepted study results indicate a significant improvement in mobility and pain difficulties.
3. The researchers stated that the participants in the intervention group reported a reduction in mobility
difficulty at week 12. Was this result statistically significant,...

...do a varianceanalysis to better understand the plant performance compared to the previous year. The main problem in related to this case is about the falling in revenues, the performance of coal-plant, the price of coal and the quality of coal. All of this problem will be answered in the next sections in the qualitative analysis of Luotang Power.
VARIANCEANALYSIS
QUANTITY VARIANCE
Thevarianceanalysis is defined as the difference between the expected amount and the actual amount of costs or revenues. Varianceanalysis uses this standard or expected amount versus the actual amount to judge performance. The analysis includes an explanation of the difference between actual and expected figures as well as an evaluation as to why the variance may have occurred. The purpose of this detailed information is to assist managers in determining what may have gone right or wrong and to help in future decision-making
Quantity Variance = (Net Generation MWh in Current Year - Net Generation MWh in
Year) x Price per MWh in Prior Year
2011
(3,427,351-3,937,377)x(0.3817)=194,676 MWh (unfavorable)
2010
(3,937,377-3,028,690)x(0.4186)=380,376 MWh (favorable)
Based on analysis of quantity variance, in 2011 showed that unfavorable variance...

...DESIGN AND ANALYSIS OF EXPERIMENTS
TERM PROJECT PROPOSAL
Subject: Statistical analysis of a sling regarding three factors with three levels.
Aim: Our aim is to statistically analyse the effects of three factors; rubber type, shooting range and tensile distance on the shooting range.
Description: In our project, we will design three slings for three types of rubbers.With these slings, we will try three shooting angles;30, 45, 60 degrees. Also with these factors we will make experiments with three tensile distances, namely the distance that we will pull the rubber; 2, 4 and 6 cm. As response values we will use the range that particular object goes. We will use the same pebble. So there will be no difference in the trials with respect to the used object.
Thus, in the analysis, we will examine the effects of rubber, angle and the distance on the range of the object takes after being released from the sling.
At the end, we will use Design Expert software for ANOVA and interpretations from the related graphs for concluding remarks from the experiment regarding the factors.
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PROJECT ANALYSIS
As we defined in the outline, we evaluated the effects of three factors such as; rubber type, angle and tensile for the shooting range of a sling. From our experiments we got 81 response values with different levels of the factors.
The structure of the experiment and data can be...

...PROBLEM ON VARIANCEANALYSIS
[pic]
Submitted to:
PROF. ROSFE CORLAE D. BADUY
Submitted by:
ADRIAN ERWIN M. PEGASON
ERWIN S. FLORES
BETA COMPANY
Beta Company produces two products, A and B, each of which uses materials X and Y. The following unit standard costs apply:
| |Material X |Material Y |Direct Labor |
|Product A |4 lbs @ $15 |1 lb @ $9.50 |1/5 hr @ $18 |
|Product B |6 lbs @ $15 |2 lbs @ $9.50 |1/3 hr @ $18 |
During November 4,200 units of A and 3,600 units of B were produced. Also, 39,000 pounds of X were purchased at $14.40, and 11,000 pounds of Y were purchased at $9.70; all of these materials (but no other materials) were used for the month’s production. This production required 2,025 direct labor-hours at $17.50.
Questions:
1. Calculate the material price variance and usage variances for the month.
2. Calculate the labor rate and efficiency variances for the month.
3. How would your answers to Questions 1 and 2 change if you had been told that November’s planned production activity was 4,000 units of A and 4,000 units of B?
4. How would your answers to question 1 and 2 change if you had been told...