**Scenario Description:**Andre recently found a die (the traditional, six-sided variety) at the park. He took it home and rolled it 100 times and recorded the results (found in the table below). Is this a 'fair die' or has it been tampered with? Test at the \(\alpha = 0.10\) level of significance.**Hypotheses Options:**1. \(\mathbf{H_0:}\) The die is a fair die; \(\mathbf{H_1:}\) The die has been tampered with.2. \(\mathbf{H_0: \mu_1 = \mu_2;}\) \(\mathbf{H_1: \mu_1 \neq \mu_2}\)3. \(\mathbf{H_0: p_1 = p_2;}\) \(\mathbf{H_1: p_1 \neq p_2}\)4. \(\mathbf{H_0:}\) The die has been tampered with; \(\mathbf{H_1:}\) The die is a fair die.**Roll Count Table:**\[\begin{array}{|c|c|}\hline\text{Rolled} & \text{Count} \\\hline1 & 1 \\2 & 8 \\3 & 5 \\4 & 3 \\5 & 3 \\6 & 80 \\\hline\end{array}\]**Test Statistic (2 decimals):**[Input field for the test statistic]**P-value (4 decimals - if less than 0.001 answer 0):**[Input field for the P-value]**Decision on Null Hypothesis:**- [ ] Reject the Null Hypothesis- [ ] Do not Reject the Null Hypothesis**Conclusion:**- [ ] There is not enough evidence to suggest that the die has been tampered with.- [ ] There is enough evidence to suggest that the die has been tampered with.**Diagram Explanation:**The table outlines the number of times each face of the die appeared out of 100 rolls. The counts are highly skewed, with the number '6' appearing 80 times, suggesting potential tampering if the die was expected to be fair with an equal distribution of outcomes.

Name: **Scenario Description:**Andre recently found a die (the traditional,
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Description: **Scenario Description:**Andre recently found a die (the traditional, six-sided variety) at the park. He took it home and rolled it 100 times and recorded the results (found in the table below). Is this a 'fair die' or has it been tampered with? Tes

The correct hypothesis are, H0: The die is a fair die H1: The die has been tampered with. We reject the null hypothesis Chi-square value > Chi-square critical value.From the provided count data we have, Rolled Count(Oi) Ei (Oi-Ei) ((Oi-Ei)^2)/Ei 1 1 16.67 -15.67 14.729988 2 8 16.67 -8.67 4.509232154 3 5 16.67 -11.67 8.16970006 4 3 16.67 -13.67 11.20989202 5 3 16.67 -13.67 11.20989202 6 80 16.67 63.33 240.5932154 Total 100 100.02 290.4219196The test statistic is given by, χ2=∑i(Oi-Ei)2Ei =290.42 The test statistic is 290.42 The chi-square critical value with ∝ = 0.10 and 5 degrees of freedom is 9.236357. (Degrees of freedom = k-1 = 6 – 1 = 5) The chi-square value is larger than the chi-square critical value. The p-value is computed using excel function as below: Thus, the p-value = 0 The p-value is less than ∝ = 0.10. Thus, we reject the null hypothesis. Hence, we conclude that there is enough evidence to suggest that the die has been tampered with.

Math

Statistics

Andre recenty found a die (the traditional, six-sided variety) at the park. He took it home and rolled it 100 times and recorded the results (found in the table below). Is this a 'fair die' or has it been tampered with? Test at the a = 0.10 level of significance. Which would be correct hypotheses for this test? O Ho: The die is a fair die; H,: The die has been tampered with |Ho: 41 = 42; H:41 # H2 | Ho: P1 = P2; H1:P1 + P2 O Họ: The die has been tampered with; H,: The die is a fair die Roll count: Rolled Count 1 2 3 5 4 3 3 6. 80 Test Statistic (2 decimals): Give the P-value (4 decimals - if less than 0.001 answer 0): Which is the correct result: O Reject the Null Hypothesis ODo not Reject the Null Hypothesis Which would be the appropriate conclusion?

Andre recenty found a die (the traditional, six-sided variety) at the park. He took it home and rolled it 100 times and recorded the results (found in the table below). Is this a 'fair die' or has it been tampered with? Test at the a = 0.10 level of significance. Which would be correct hypotheses for this test? O Ho: The die is a fair die; H,: The die has been tampered with |Ho: 41 = 42; H:41 # H2 | Ho: P1 = P2; H1:P1 + P2 O Họ: The die has been tampered with; H,: The die is a fair die Roll count: Rolled Count 1 2 3 5 4 3 3 6. 80 Test Statistic (2 decimals): Give the P-value (4 decimals - if less than 0.001 answer 0): Which is the correct result: O Reject the Null Hypothesis ODo not Reject the Null Hypothesis Which would be the appropriate conclusion?

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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