### Chi-Square Test for a Fair DieA gambler rolls a die to determine whether or not it is fair. A fair die is one that does not favor any of the 6 numbers. Test at 10% significance to see if the die is weighted. Round to the fourth as needed.#### Data CollectedThe observed and expected frequencies are shown in the table below:| Categories | Observed Frequency | Expected Frequency ||------------|---------------------|---------------------|| 1 | 76 | || 2 | 73 | || 3 | 54 | || 4 | 67 | || 5 | 50 | || 6 | 76 | |#### AnalysisTo determine if the die is fair, we need to perform a Chi-Square test. The fields provided for the educational exercise:1. **Test Statistic**: - Calculate the test statistic \( \chi^2 \) using the formula: \[ \chi^2 = \sum \frac{(O_i - E_i)^2}{E_i} \] where \( O_i \) is the observed frequency and \( E_i \) is the expected frequency.2. **Degrees of Freedom**: - Calculate the degrees of freedom \( df \) using the formula: \[ df = n - 1 \] where \( n \) is the number of categories (in this case, 6).3. **p-val**: - The p-value will be determined based on the Chi-Square distribution table corresponding to the calculated test statistic and degrees of freedom.4. **Decision Rule**: - Select an answer to decide whether or not the null hypothesis is rejected based on the p-value and the significance level.5. **Did something significant happen?** - Decide if there is enough evidence to conclude whether the die is fair or not.By filling in the above values, we can determine if the deviation observed in the data is significant enough to conclude that the die is not fair.

Introduction: Denote p1, p2, p3, p4, p5, and p6 as the respective true proportions of obtaining the…

A gambler rolls a die to determine whether or not it is fair. A fair die is one that does not favor any of the 6 numbers. Test at 10% significance to see if the die is weighted. Round to the fourth as needed. Observed Expected Categories Frequency Frequency 1 76 2 73 3 54 4 67 5 50 6 76 Test Statistic: Degrees of Freedom: p-val: Decision Rule: | Select an answer Did something significant happen? Select an answer There Select an answer enough evidence to conclude ( Select an answer

A gambler rolls a die to determine whether or not it is fair. A fair die is one that does not favor any of the 6 numbers. Test at 10% significance to see if the die is weighted. Round to the fourth as needed. Observed Expected Categories Frequency Frequency 1 76 2 73 3 54 4 67 5 50 6 76 Test Statistic: Degrees of Freedom: p-val: Decision Rule: | Select an answer Did something significant happen? Select an answer There Select an answer enough evidence to conclude ( Select an answer

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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