Statistical Analysis Report
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: H_{0}: The average number of transformers is 745.
Alternative hypothesis: H_{a}: The average number of transformers is less than 745.
H_{0}: µ = 745 versus H_{a}: 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:
- 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.
- 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.
- We reject the null hypothesis that there is no any significant difference in the average number of transformers for the given three years.
- 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 |