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Contingency Table: Formulas and Concepts

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The following problems are intended to help you continue working with formulae and concepts pertaining to contingency tables (bivariate frequency tables). Good luck and enjoy!

Results on seat belt usage from the 2003 Youth Risk Behavior Survey were published in a USA Snapshot on January 13, 2005. The following table outlines the results from the high school students who were surveyed in the state of Nebraska. They were asked whether or not they rarely or never wear seat belts when riding in someone else's car (Johnson & Kuby, 2007).

(See attached file for data)

1. Fill in the remainder of the table (find the totals). How many total students were surveyed for this study?
2. What are the two variables in this study? Which one is the independent variable and which is the dependent variable? How do you know? Explain briefly.
3. What percentage of women rarely or never use their seatbelts? Please show your work.
4. What percentage of men rarely or never use their seatbelts? Please show your work.
5. Does it appear that there is a significant difference in the percentage of men and women who rarely or never wear their seatbelts? Explain.
6. What percentage of women usually or always use their seatbelts? Please show your work.
7. What percentage of men usually or always use their seatbelts? Please show your work.
8. Does it appear that there is a significant difference in the percentage of men and women who usually or always wear their seatbelts? Explain.
9. Based on your answers above, and the results of a hypothesis test for the contingency table above, does it appear that the independent variable affects the dependent variable? Explain
10. Interpret the results in the context of the problem.

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Solution Summary

The expert examines contingency table formulas and concepts.

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  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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