**Chi-Square Test for Independence: Analysis of Categorical Variables**In a study analyzing the relationship between two categorical variables, $X =$ course subject and $Y =$ grade earned by a student, researchers selected $n = 800$ students. The study examined $m = 4$ distinct courses and $k = 6$ grades, from $A$ to $F$ and $W$. To test the independence between $X$ and $Y$, they calculated a chi-square ($\chi^2$) test statistic of:\[ \text{TS} = 29.64 \]The primary question is whether, at the significance level $\alpha = 0.01$, there is sufficient evidence to conclude that $X$ and $Y$ are dependent.**Steps to Analyze the Test:**1. **Critical Value:** - Determine the critical value (or values) necessary for this procedure, based on degrees of freedom and the significance level.2. **Rejection Rule:** - Formulate the rejection rule for the test, using the critical value to decide if the null hypothesis should be rejected.3. **Decision Making:** - State your decision regarding the null hypothesis of independence, considering the calculated test statistic and the significance level $\alpha = 0.01$.**Solution:**To solve this problem, calculate the degrees of freedom for the chi-square test using the formula:\[ \text{df} = (m - 1)(k - 1) \]Next, find the critical value from the chi-square distribution table corresponding to $\alpha = 0.01$ and the calculated degrees of freedom. Compare the test statistic to this critical value to determine whether to reject the null hypothesis of independence.This approach provides a step-by-step method to assess the dependency between course subjects and grades earned by students.

Answered: Analysis of whether two categorical…

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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A bank conducts a survey in which it randomly samples 400 of its customers. The survey asks the customers which way they use the bank the most: (1) interacting with a teller at the bank, (2) using ATM's or (3) using the bank's online banking service. It also asks their level of satisfaction with the service they most often use (on a scale of 0-10 with 0= very poor and 10=excellent). Does mean satisfaction differ according to how they most use the bank? a) Identifying notation, state the null hypothesis and alternative hypothesis for conducting an ANOVA with data from the survey. b) Report the df values for this ANOVA. Above what F statistic values give a P=value below 0.05? c) For the data, F=0.46 and the P-value equals 0.63. what can you conclude? d)What were the assumptions on which the ANOVA was based? Which assumption is the most important? e) based on answer C, do you think it is necessary to conduct Tukey's multiple comparisons? Why or why not?
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