Problem Statement
A case study was conducted by a manufacturing company, Ace Inc., that specializes in circuit boards used in security devices. The study aims to determine basic math competency of its production line workers. A random sample of 71 production line employees were chosen for the survey and the test data results were collected accordingly. The resulting data also includes whether each employee in the sample took a statistics course or not. Ace would like to examine this data in order to prepare analysis report to the management team.
Statistical Results
1. In this study of test scores and took statistics course, each variable in the sample data is characterized by creating a histogram and pie chart, respectively. According to the “Histogram of Test Scores”, Appendix A(2), the data can be described as normally distributed. The descriptive statistics result for the variable “Test Scores” in Appendix A (1), also indicates that the distribution is symmetric around the mean, with the mean value of 52.6 points and the median 51 points. This shows that the data values appear to be close to the center of the data and that there are no extreme data values in the sample that might have pulled the mean upwards from the center. The normal approaches the horizontal axis on either side of the mean. Therefore, in this sample the data can be characterized by the mean and standard deviation, the variable of interest “Test Scores” can be treated as continuous variable and the distribution as normal. Similarly, the “Pie Chart of Took Statistics” in Appendix B, illustrates the number of employees who took statistics course or not. …show more content…
The chart is constructed by dividing the circle into two slices, indicating those who took statistics course (1) or those who do not (0). Each slice is proportional to the percentage share of the total sample count. This value can be used to calculate the proportion of those who took statistics course, Appendix D(2). The pie chart also shows that majority of the employees did not take statistics course (52 ≈ 73 %). Only a small number of employees (19 ≈ 27 %) indicated that they have taken statistics course before taking the basic math competency test. The analysis of this sample data using pie chart is important because it clearly shows the responses with respect to the total number of employees in the sample. 2. According to the manual calculation in Appendix D(1), the estimated confidence interval with 95 percent confidence level is between 48.91 and 56.31. This result validates the computer generated (Mini Tab) results shown in Appendix C(1). Therefore, based on the sample data of 71 employees, with 95 percent confidence level the true average test score is between 48.91 and 56.31 points. The single valued estimate of the sample mean shown in Appendix C(1), which is 52.61 is also in between the confidence interval. 3. The claim that shows an average test score of 70 points for all employees is not acceptable based on the confidence interval calculation. According to the calculation, Appendix D (1), with 95 percent confidence the average test score is between 48.91 and 56.31. The maximum value for the average test score is 56.31, which is less than 70. Therefore the probability of having an average of 70 points for all employees is very low. Thus, the claim can be
A case study was conducted by a manufacturing company, Ace Inc., that specializes in circuit boards used in security devices. The study aims to determine basic math competency of its production line workers. A random sample of 71 production line employees were chosen for the survey and the test data results were collected accordingly. The resulting data also includes whether each employee in the sample took a statistics course or not. Ace would like to examine this data in order to prepare analysis report to the management team.
Statistical Results
1. In this study of test scores and took statistics course, each variable in the sample data is characterized by creating a histogram and pie chart, respectively. According to the “Histogram of Test Scores”, Appendix A(2), the data can be described as normally distributed. The descriptive statistics result for the variable “Test Scores” in Appendix A (1), also indicates that the distribution is symmetric around the mean, with the mean value of 52.6 points and the median 51 points. This shows that the data values appear to be close to the center of the data and that there are no extreme data values in the sample that might have pulled the mean upwards from the center. The normal approaches the horizontal axis on either side of the mean. Therefore, in this sample the data can be characterized by the mean and standard deviation, the variable of interest “Test Scores” can be treated as continuous variable and the distribution as normal. Similarly, the “Pie Chart of Took Statistics” in Appendix B, illustrates the number of employees who took statistics course or not. …show more content…
The chart is constructed by dividing the circle into two slices, indicating those who took statistics course (1) or those who do not (0). Each slice is proportional to the percentage share of the total sample count. This value can be used to calculate the proportion of those who took statistics course, Appendix D(2). The pie chart also shows that majority of the employees did not take statistics course (52 ≈ 73 %). Only a small number of employees (19 ≈ 27 %) indicated that they have taken statistics course before taking the basic math competency test. The analysis of this sample data using pie chart is important because it clearly shows the responses with respect to the total number of employees in the sample. 2. According to the manual calculation in Appendix D(1), the estimated confidence interval with 95 percent confidence level is between 48.91 and 56.31. This result validates the computer generated (Mini Tab) results shown in Appendix C(1). Therefore, based on the sample data of 71 employees, with 95 percent confidence level the true average test score is between 48.91 and 56.31 points. The single valued estimate of the sample mean shown in Appendix C(1), which is 52.61 is also in between the confidence interval. 3. The claim that shows an average test score of 70 points for all employees is not acceptable based on the confidence interval calculation. According to the calculation, Appendix D (1), with 95 percent confidence the average test score is between 48.91 and 56.31. The maximum value for the average test score is 56.31, which is less than 70. Therefore the probability of having an average of 70 points for all employees is very low. Thus, the claim can be