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.)![Image](X^2 Distribution)The graph depicted is a Chi-Square (χ²) Distribution. The x-axis represents the χ² values ranging from 0 to 139, while the y-axis indicates the probability density, ranging from 0 to 0.12. The curve shows a typical Chi-Square distribution shape, starting low, peaking, and then gradually tapering off.### Fields to Fill:- \( X^2 \) value: [____] \( \chi^2_{(\alpha, df)} = \) [____] *(Round to three decimal places.)*- Test Statistic = [____] *(Round to three decimal places.)*- p-value = [____] *(Round to four decimal places.)*### Decision:Select an answer from a dropdown menu.### Conclusion:Select an answer from a dropdown regarding the claim that all 5 categories are equally likely to be selected. You are conducting a multinomial Goodness of Fit hypothesis test for the claim that all 5 categories are equally likely to be selected at the 0.1 significance level. Complete the table. Report all answers correct to three decimal places.| Category | Observed Frequency | Expected Frequency | \(\frac{{(O-E)^2}}{E}\) ||----------|--------------------|--------------------|--------------------------------|| A | 24 | | || B | 25 | | || C | 14 | | || D | 18 | | || E | 20 | | |\(H_0\): \(P_A = P_B = P_C = P_D = P_E\)\(H_1\): at least one is differentOriginal claim = [Select an answer]

Name: Enter the critical value, along with the significance level and degre
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Description: 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.)![Image](X^2 Distribution)The graph depicted is a Chi-Square (χ²) Dist

The claim of the test is that all 5 categories are equally likely to be selected indicating that the null hypothesis is the original claim. Thus, the original claim is null hypothesisH0. The expected frequencies are, Category Observed Frequency Expected Frequency O-E2E A 24 1015=20.2 24-20.2220.2=0.715 B 25 1015=20.2 25-20.2220.2=1.141 C 14 1015=20.2 14-20.2220.2=1.903 D 18 1015=20.2 18-20.2220.2=0.240 E 20 1015=20.2 20-20.2220.2=0.002 Total 101 The degrees of freedom is, df=k-1=5-1=4 The degrees of freedom is 4. The significance level is 0.10. Computation of Critical value: The critical value of χ2-distribution with 0.10 level of significance at 4 degrees of freedom can be obtained using the excel formula “=CHISQ.INV.RT(0.1,4)”. The critical value is 7.779. The graph is, The test statistic is, χ2=Sum of O-E2E=0.715+1.141+1.903+0.240+0.002=4.001 Thus, the test statistic is 4.001. Computation of P-value: The p-value of χ2-distribution for 4.001 at 4 degrees of freedom can be obtained using the excel formula “=CHISQ.DIST.RT(4.001,4)”. The p-value is 0.4059. Decision rule: If p-value≤α, then reject the null hypothesis. Otherwise, do not reject the null hypothesis. Conclusion: The p-value (0.4059) is greater than the level of significance (0.10). Based on decision rule, fail to reject the null hypothesis. Thus, it can be concluded that the claim that all 5 categories are equally likely to be selected.

Math

Statistics

You are conducting a multinomial Goodness of Fit hypothesis test for the claim that all 5 categories are equally likely to be selected at the 0.1 significance level. Complete the table. Report all answers correct to three decimal places.

You are conducting a multinomial Goodness of Fit hypothesis test for the claim that all 5 categories are equally likely to be selected at the 0.1 significance level. Complete the table. Report all answers correct 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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