**Title: Chi-Square Test for Independence: Educational Exercise on Contingency Tables**The following exercise provides a practical approach to understanding the chi-square test for independence. We use a contingency table displaying the results of a random sample of high school students categorized by year and grade point average. The task is to test, at a significance level of \( \alpha = 0.05 \), the claim that there is a dependency between at least two of the variables.**Hypothesis Testing:**- **Null Hypothesis (\( H_0 \)):** The variables are independent.- **Alternative Hypothesis (\( H_a \)):** At least two of the variables are dependent (claim).**Instructions:**1. **Use the Independence \#2 Calculator:** - Fill in the contingency table for the rows and columns based on the results. - Input the level of significance \( \alpha = 0.05 \).2. **Tasks:** a.) **Find the Degrees of Freedom, Critical Value, and Rejection Region:** - Determine the degrees of freedom for the contingency table. - Find the corresponding critical value using the chi-square distribution table. - Identify the rejection region based on the critical value and \( \alpha \). b.) **Find the Chi-Square Test Statistic:** - Calculate the test statistic using the formula for chi-square tests. c.) **Assess the Test Statistic:** - Check if the test statistic falls within the rejection region. - Provide reasoning for your conclusion. d.) **Decision on the Null Hypothesis:** - Based on the test statistic, choose to reject or fail to reject the null hypothesis. e.) **Conclusion Statement:** - Discuss if there is sufficient evidence to support the claim of dependency between the variables. - Provide a comprehensive conclusion including the level of significance \( \alpha = 0.05 \).This exercise is designed to enhance understanding of hypothesis testing and contingency tables, guiding learners through practical statistical analysis. The table presents a distribution of students across different GPA ranges segmented by academic year level: Freshman, Sophomore, Junior, and Senior.| GPA Range | Freshman | Sophomore | Junior | Senior ||-----------|----------|-----------|--------|--------|| Less than 1.00 | 20 | 24 | 20 | 18 || 1.00 - 1.99 | 40 | 40 | 44 | 58 || 2.00 - 2.99 | 93 | 90 | 87 | 83 || 3.00 - 3.99 | 125 | 105 | 116 | 117 || 4.00 + | 38 | 23 | 24 | 33 |- **Freshmen** have the highest count in the 3.00 - 3.99 GPA range (125 students) and the lowest in the Less than 1.00 range (20 students).- **Sophomores** also peak in the 3.00 - 3.99 range (105 students), but their count in the 4.00+ range is the lowest (23 students).- **Juniors** follow a similar pattern with the greatest number in the 3.00 - 3.99 range (116 students) and the least in the Less than 1.00 range (20 students).- **Seniors** show a maximum in the 3.00 - 3.99 range (117 students) and a minimum in the Less than 1.00 range (18 students).Overall, most students across all levels fall in the 3.00 - 3.99 GPA range, while the number decreases significantly in the Less than 1.00 range.

Answered: The contingency table shows the results…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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I need the p value Thankyou so much
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Z?
A case-control (or retrospective) study was conducted to investigate a relationship between the colors of helmets worn by motorcycle drivers and whether they are injured or killed in a crash. Results are given in the accompanying table. Using a 0.01 significance level, test the claim that injuries are independent of helmet color. D Black Color of Helmet Yellow 32 Blue White 331 Controls (not injured) Red 159 482 100 Cases (injured or 211 109 8 65 47 killed) Click here to view the chi-square distribution table. Identify the null and alternative hypotheses. Choose the correct answer below. O A. Ho: Whether a crash occurs and helmet color are dependent H₁: Whether a crash occurs and helmet color are independent OB. Ho: Injuries and helmet color are dependent H₁: Injuries and helmet color are independent OC. Ho: Whether a crash occurs and helmet color are independent H₁: Whether a crash occurs and helmet color are dependent O D. Ho: Injuries and helmet color are independent H₁: Injuries…
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