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# Statistical Analysis Report

Introduction:

The statistical analysis is very important for decision making in every industry or business. It plays an important role in the each section and department for making a better decisions and it helps in increasing the profit and quality of the products and services. Here, we want to analyse the data for the A-CAT Corporation for the variables such as number of transformers and demand. For the analysis purpose, we have to analyse this data by using the different statistical tools and techniques. We have to use the descriptive statistics, inferential statistics or testing of hypothesis, one way ANOVA and regression analysis for the given data for the A-CAT Corporation. Let us see this statistical data analysis in detail explained in the next topics.

Statistical Analysis:

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In this topic, we have to see the statistical analysis for the variables regarding the A-CAT corporation. We have to use the descriptive statistics, testing of hypothesis, one way analysis of variance and regression analysis. First of all we have to see the descriptive statistics for the variable number of transformers. The descriptive statistics for the number of transformers is summarised as below:

The average number of transformers is given as 801.1667 with the standard deviation of 83.7885. The minimum number of transformers is given as 695 while the maximum number of transformers is given as 916.

Now, we want to check the hypothesis or claim whether the average number of transformers is less than 745 or not. To check this hypothesis or claim we need to use the one sample t test for the population mean. We use the t test because we don’t know the information about the population standard deviation. The null and alternative hypothesis for this test is given as below:

Null hypothesis: H0: The average number of transformers is 745.

Alternative hypothesis: Ha: The average number of transformers is less than 745.

H0: µ = 745 versus Ha: µ < 745

For this test we assume the level of significance or alpha value as 0.05 or 5%.

The test statistic formula for this test is given as below:

Test statistic = t = (xbar – population mean) / [sample SD / sqrt(n)]

Now, by plugging all values in this formula we get the test statistic value and other values regarding this test as below:

 t Test for Hypothesis of the Mean Data Null Hypothesis                m= 745 Level of Significance 0.05 Sample Size 12 Sample Mean 801.1667 Sample Standard Deviation 83.7885 Intermediate Calculations Standard Error of the Mean 24.1877 Degrees of Freedom 11 t Test Statistic 2.3221 Lower-Tail Test Lower Critical Value -1.7959 p-Value 0.9798 Do not reject the null hypothesis

Here, we get the p-value as 0.9798 which is greater than the given level of significance or alpha value 0.05, so we do not reject the null hypothesis that the average number of transformers is 745. This means, there is no evidence that the average number of transformers is less than 745.

Now, we have to check the claim whether there is any significant difference in the average number of transformers for the years 2006, 2007 and 2008. For checking this claim, we have to use the one way analysis of variance. The ANOVA table for this test is given as below:

 ANOVA: Single Factor SUMMARY Groups Count Sum Average Variance Year 2006 12 9614 801.1666667 7020.5152 Year 2007 12 10784 898.6666667 18750.0606 Year 2008 12 11884 990.3333333 21117.8788 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 214772.2222 2 107386.1111 6.8707 0.0032 3.2849 Within Groups 515773.0000 33 15629.4848 Total 730545.2222 35 Level of significance 0.05

For this ANOVA table we get the p-value as 0.0032 which is less than the given level of significance or alpha value 0.05, so we reject the null hypothesis that there is no any significant difference in the average number of transformers for the given three years. This means we conclude that there is a significant difference in the average number of transformers for the given three years.

Now, we have to use the regression analysis for the purpose of prediction of the transformers requirements based on the sales of refrigerators. The regression analysis for this model is given as below:

 Simple Linear Regression Analysis Regression Statistics Multiple R 0.9259 R Square 0.8574 Adjusted R Square 0.8495 Standard Error 179.4679 Observations 20 ANOVA df SS MS F Significance F Regression 1 3485332.9249 3485332.9249 108.2109 0.0000 Residual 18 579756.8751 32208.7153 Total 19 4065089.8000 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 1233.4995 167.4755 7.3653 0.0000 881.6465 1585.3524 Sales of Refrigerators 0.3149 0.0303 10.4024 0.0000 0.2513 0.3785

For this regression model, we get the p-value as 0.00 which is less than the given level of significance so we reject the null hypothesis that there is no any significant relationship exists between the given two variables. The correlation coefficient between the two variable transformer requirements and the sales of refrigerator is given as 0.9259 which means there is a strong positive relationship or linear association exists between the given two variables. The coefficient of determination or the value of R square is given as 0.8574 which means about 85.74% of the variation in the dependent variable transformers requirements is explained by the independent variable sales of refrigerators.

Conclusions:

1. The average number of transformers is given as 801.1667 with the standard deviation of 83.7885. The minimum number of transformers is given as 695 while the maximum number of transformers is given as 916.
2. We get the p-value as 0.9798 which is greater than the given level of significance or alpha value 0.05, so we do not reject the null hypothesis that the average number of transformers is 745. This means, there is no evidence that the average number of transformers is less than 745.
3. We reject the null hypothesis that there is no any significant difference in the average number of transformers for the given three years.
4. We reject the null hypothesis that there is no any significant relationship exists between the given two variables. The correlation coefficient between the two variable transformer requirements and the sales of refrigerator is given as 0.9259 which means there is a strong positive relationship or linear association exists between the given two variables. The coefficient of determination or the value of R square is given as 0.8574 which means about 85.74% of the variation in the dependent variable transformers requirements is explained by the independent variable sales of refrigerators.

Appendix:

 Year 2006 Year 2007 Year 2008 779 845 857 802 739 881 818 871 937 888 927 1159 898 1133 1072 902 1124 1246 916 1056 1198 708 889 922 695 857 798 708 772 879 716 751 945 784 820 990
 Sales of Refrigerators Transformer requirements 3832 2399 5032 2688 3947 2319 3291 2208 4007 2455 5903 3184 4274 2802 3692 2343 4826 2675 6492 3477 4765 2918 4972 2814 5411 2874 7678 3774 5774 3247 6007 3107 6290 2776 8332 3571 6107 3354 6792 3513

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