**Chi-Square Goodness-of-Fit Test for a Fair Dice at 0.01 Significance Level**The goal is to test the claim that a six-sided die is fair at the 0.01 significance level. Complete the table by rounding all answers to three decimal places.| Number Rolled on Dice | Observed Frequency | Expected Frequency | \( \frac{(O - E)^2}{E} \) ||-----------------------|--------------------|---------------------|---------------------------|| 1 | 11 | | || 2 | 24 | | || 3 | 25 | | || 4 | 11 | | || 5 | 18 | | || 6 | 25 | | |**Hypotheses:**- \( H_0 \): All sides of the dice are equally probable: \( p_1 = p_2 = p_3 = p_4 = p_5 = p_6 \)- \( H_1 \): At least one side has a different probability.**Original Claim:** Select an answer.---To complete the analysis, calculate the expected frequency for each side under the null hypothesis and use the chi-square formula to determine the goodness-of-fit statistic. Compare this statistic against the chi-square distribution with \( \alpha = 0.01 \) to test the hypothesis. **Chi-Square Test on an Educational Website****Instructions:**Enter the critical value, along with the significance level and degrees of freedom \(\chi^2 (\alpha, df)\) below the graph. (Graph is for illustration only. No need to shade.)**Graph Explanation:**The graph illustrates a Chi-Square (\(X^2\)) Distribution. The x-axis represents the values of \(X\) ranging from 0 to 139. The y-axis represents the probability ranging from 0 to 0.12. The shape of the distribution is skewed to the right, with a peak around a probability of 0.1.**Fill in the Blanks:**- \(\chi^2 (\alpha, df) =\) [Input Field]*(Round to three decimal places.)*- Test Statistic = [Input Field]*(Round to three decimal places.)*- p-value = [Input Field]*(Round to four decimal places.)***Decision:**[Dropdown Menu to Select an Answer]**Conclusion:**[Dropdown Menu to Select an Answer] the claim that all 6 categories are equally likely to be selected.---This page is designed to help students understand how to perform and interpret a Chi-Square test by filling in the necessary values based on their calculations.

The claim of the test is that a six-sided dice is fair at the 0.01 significance level. The original claim is null hypothesis. Thus, the original claim is H0. The degrees of freedom is, df=k-1=6-1=5 The degrees of freedom is 5. The critical value of χ2 for 0.01 level of significance at 5 degrees of freedom can be obtained using the excel formula “=CHISQ.INV.RT(0.01,5)”. The critical value is 15.086. Thus, the critical value is χ0.01,52=15.086. The expected frequency is, Number rolled on die Observed frequency Expected frequency O-E2E 1 11 1146=19 11-19219=3.368 2 24 1146=19 24-19219=1.316 3 25 1146=19 25-19219=1.895 4 11 1146=19 11-19219=3.368 5 18 1146=19 18-19219=0.053 6 25 1146=19 25-19219=1.895 Total 114 The test statistic is, χ2=Sum ofO-E2E=3.368+1.316+1.895+3.368+0.053+1.895=11.895 Thus, the test statistic is 11.895. Computation of p-value: The p-value of χ2-distribution at 5 degrees of freedom can be obtained using the excel formula “=CHISQ.DIST.RT(11.895,5)”. The p-value is 0.0363. Thus, the p-value is 0.0363. Decision rule: If p-value≤α, then reject the null hypothesis. Otherwise, do not reject the null hypothesis. Conclusion: The p-value (0.0363) is less than the level of significance (0.01). Based on decision rule, fail to reject the null hypothesis. Thus, it can be concluded that the claim that all 6 categories are equally likely to be selected.

Answered: Test the claim that a six-sided dice is…

Math

Statistics

Test the claim that a six-sided dice is fair at the 0.01 significance level. Complete the table. Round all answers to three decimal places.

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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