Individual Paper #3: Non parametric and Chi-square distribution

Brief Summary:
I worked for a logistic company. My major responsibility was in charge of the storage and transportation of parts of cars between two areas, which are about 1400 miles apart. One of my jobs is collecting the goods from suppliers and arranging the trucks to deliver them. There are five truck drivers, and each of them is assigned to deliver on each weekday throughout a whole year. Before the delivery, we will check the quality of the goods and Make sure that there are no damaged goods. When arriving at the destination, the staff will check the goods again and record the damaged goods that occurred in transit. At the end of every month, we will pay for the compensation according to the number of the defective goods. In order to reduce the number of the damaged goods during the delivery, I want to identify the reasons why they are damaged. In this study, I want to find out that whether some drivers are more prone to make the goods damaged during their delivery.

Variable to be measured:
Two variables are to be measured. The first variable is just the five truck drivers, and the second one is the quality of the goods after the delivery.

Determination of Population:
Population in this case is defined as the all goods delivered from Tianjin area to Guangzhou area.

Statistical method:
To analyze relationship between the two variables above which are both nominal in terms of data type, I decide to use Chi-squared test of a contingency table.

Sample Selection:
The information about delivery is recorded in our computer system, including the delivery date, name of the driver, the number of damaged goods and so on. I take out the data about 52 weeks during the previous year and record them into the following table:

...Chisquare test for independence of two attributes. Suppose N observations are considered and classified according two characteristics say A and B. We may be interested to test whether the two characteristics are independent. In such a case, we can use Chisquare test for independence of two attributes.
The example considered above testing for independence of success in the English test vis a vis immigrant status is a case fit for...

...Chi-square requires that you use numerical values, not percentages or ratios.
Then calculate 2 using this formula, as shown in Table B.1. Note that we get a value of 2.668 for 2. But what does this number mean? Here's how to interpret the 2 value:
1. Determine degrees of freedom (df). Degrees of freedom can be calculated as the number of categories in the problem minus 1. In our example, there are two categories (green and yellow); therefore, there is I degree...

...CHI-SQUARE TEST (χ²):
Chi-square is a statistical test commonly used to compare observed data with data we would expect to obtain according to a specific hypothesis. For example, if, according to Mendel's laws, you expected 10 of 20 offspring from a cross to be male and the actual observed number was 8 males, then you might want to know about the "goodness to fit" between the observed and expected. Were the deviations (differences...

...2.3. The Chi-SquareDistribution
One of the most important special cases of the gamma distribution is the chi-squaredistribution because the sum of the squares of independent normal random variables with mean zero and standard deviation one has a chi-squaredistribution. This section collects some basic properties of...

...Chi-Square Test
Chi-square is a statistical test commonly used to compare observed data with data we would expect to obtain according to a specific hypothesis. For example, if, according to Mendel's laws, you expected 10 of 20 offspring from a cross to be male and the actual observed number was 8 males, then you might want to know about the "goodness to fit" between the observed and expected. Were the deviations (differences between...

...A chi-squared test, also referred to as chi-square test or χw² test, is any statistical hypothesis test in which the sampling distribution of the test statistic is a chi-squared distribution when the null hypothesis is true. Also considered a chi-squared test is a test in which this is asymptotically true, meaning that the sampling distribution (if the null hypothesis is true) can...

...you conduct a chi-square test of independence, what is the expected frequency count of male Independents?
b) If you conduct a chi-square test of independence, what is the expected frequency count of female Democrats?
c) If you conduct a chi-square test of independence, what is the observed count of female Independents?
d) If you conduct a chi-square test of...

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CHAPTER 14: CHI-SQUARE TESTING
STATISTICS FOR BUSINESS TAs: Vo Vuong Van Anh, Le Phuoc Thien Thanh, and Le Nhat Ho December 21, 2013
TABLE OF CONTENTS
• PART I: CHI-SQUARE TESTING FOR GOODNESS-OF-FIT. • PART II: CHI-SQUARE TESTING FOR NORMAL DISTRIBUTION. • PART III: CHI-SQUARE TESTING FOR INDEPENDENCE.
December 2013
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