Free Engineering: Statistical Analysis Report Sample

Abstract:

The main purpose of this experiment is to utilize a sample of nuts in order to determine the dimensions of the entire population. A sample representative of 179 nuts was used in order to determine whether the company created the nuts equally. Using a micrometer, the diameter of the 179 nuts were measured and recorded. The descriptive statistics for the data was determined using Excel. Random numbers were also generated and this were compared to the data collected during the experiment. T tests and an ANOVA was carried out on samples from the data collected. From the results, it is evident that the sample data is similar to the population data. This implies that the sample can be used to make statistical inferences.

Introduction:

Statistics and statistical analysis can be utilized in making inferences about a certain population. The use of limited sample data to make an inference on the population parameters is possible in the case of qualitative data analysis. Inference from the sample about the population indicate that although certain characteristics of the population could be understood by observing the sample. However, complete representation of the population is not possible by use of the sample. There is the goodness of fit test on data and although a comparison between real population data and random population, data did yield information on the relationship. For example, a company interested in introducing a new product can use statistics to determine whether the products meets consumer expectations when released. Using the results obtained from such a study an inference can be made for the entire population. For this experiment, a sample representative of 179 nuts was used in order to evaluate the statistical properties of nuts. Statistical analysis will be carried out on the data in order to determine whether the company created the nuts equally.

Procedure:

Using a micrometer, the thickness of 179 nuts was measured. The data obtained was recorded in an Excel worksheet that would be utilized for data analysis. The first step in the data analysis was to determine the mean, median, and mode, standard deviation, and variance of the data.
The Chauvenet’s criterion was then used to eliminate any inconsistent data points in the data collected. The data was adjusted accordingly and the mean, median, and mode, standard deviation and variance of the data was recomputed. Using equations 2 and 3 respectively, the bins and width for the histogram were determined.
Using the data analysis toolpark in Excel a histogram was developed. A normal distribution curve was added to the histogram using the NormDist function. A scatterplot of bins vs. frequency percent was created for the adjusted data. The distribution curve was then added to the graph by adding a smooth scatter plot.
A random number generator was then used to generate values between the largest and smallest nut. The RAND() function was used in generating the numbers. The random values were arranged from smallest to largest and the random values were graphed against the measured values of nut size. Using Excel the regression equation and tread line was added to the graph. The Linest function was also used to provide additional information on the goodness of fit of the regression model. The correlation coefficient was also determined.
Using the sampling tool, 2 groups of 10 sample were derived from the data set. The mean and standard deviation for both groups was determined. Using a t test the mean difference between the two samples was determined. The sampling tool was used to create another 3 groups of 10 samples each. The ANOVA tool in excel was used to test whether the means for three groups were equal.

Results and Discussion:

Examining the histogram (chart 1) and the cumulative frequency chart (chart 2) it is evident that the data is distributed throughout the entire range. The histogram also shows that the majority of the data lies close to the mean. Majority of the data points lie between the 0.7382 inches and 0.7448 inches. Using the random vs, measured chart (chart 3) it is evident that the tread line is not a perfect fit. However, it has a high R square value which is 0.793.
The results of the t test produced a p value greater than the significance value (table 5). This implies that significance has been reached and the hypothesis that there is no mean difference between the populations should be accepted. Furthermore, the p value for the two-tail test is also less than the t critical value. This implies that the sample used is an excellent representation of the entire population. Furthermore, the results obtained for the sample can be replicated for the entire population.
The results of the ANOVA indicate that there is no difference between the three samples. This implies that the mean values do not vary significantly between the three groups. The reason for this observation is that the Fcritical value is greater than the F value (table 6).
Conclusion

Appendix

Pagano, R. R. (2010). Understanding statistics in the behavioral sciences. Australia: Thomson Wadsworth.