Question Manufacturers are testing a die to make sure that it is fair (has a uniform distribution). They roll the die 72 times and record the outcomes. They conduct a chi-square Goodness-of-Fit hypothesis test at the 5% significance level. (a) The null and alternative hypotheses are: • Ho: The die has the uniform distribution. Ha: The die does not have the uniform distribution. (b) x6 = 4.500. (C) XO.05 = 11.070. ● (d) What conclusions can be made? Select all that apply. Select all that apply: We should reject Ho. We should not reject Ho. At the 5% significance level, there is sufficient evidence to conclude that the die is not fair. At the 5% significance level, there is not enough evidence to conclude that the die is not fair.
Question Manufacturers are testing a die to make sure that it is fair (has a uniform distribution). They roll the die 72 times and record the outcomes. They conduct a chi-square Goodness-of-Fit hypothesis test at the 5% significance level. (a) The null and alternative hypotheses are: • Ho: The die has the uniform distribution. Ha: The die does not have the uniform distribution. (b) x6 = 4.500. (C) XO.05 = 11.070. ● (d) What conclusions can be made? Select all that apply. Select all that apply: We should reject Ho. We should not reject Ho. At the 5% significance level, there is sufficient evidence to conclude that the die is not fair. At the 5% significance level, there is not enough evidence to conclude that the die is not fair.
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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![### Question
Manufacturers are testing a die to make sure that it is fair (has a uniform distribution). They roll the die 72 times and record the outcomes.
They conduct a chi-square Goodness-of-Fit hypothesis test at the 5% significance level.
(a) The null and alternative hypotheses are:
- \( H_0 \): The die has the uniform distribution.
- \( H_a \): The die does not have the uniform distribution.
(b) \( \chi^2_0 = 4.500. \)
(c) \( \chi^2_{0.05} = 11.070. \)
(d) What conclusions can be made? Select all that apply.
#### Select all that apply:
- [ ] We should reject \( H_0 \).
- [x] We should not reject \( H_0 \).
- [ ] At the 5% significance level, there is sufficient evidence to conclude that the die is not fair.
- [x] At the 5% significance level, there is not enough evidence to conclude that the die is not fair.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F44772e7e-8412-4f06-b2cc-17951c4d7df3%2Fe9a8992c-2ae0-4624-a066-eadc152e4f6c%2Fkwo3kv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question
Manufacturers are testing a die to make sure that it is fair (has a uniform distribution). They roll the die 72 times and record the outcomes.
They conduct a chi-square Goodness-of-Fit hypothesis test at the 5% significance level.
(a) The null and alternative hypotheses are:
- \( H_0 \): The die has the uniform distribution.
- \( H_a \): The die does not have the uniform distribution.
(b) \( \chi^2_0 = 4.500. \)
(c) \( \chi^2_{0.05} = 11.070. \)
(d) What conclusions can be made? Select all that apply.
#### Select all that apply:
- [ ] We should reject \( H_0 \).
- [x] We should not reject \( H_0 \).
- [ ] At the 5% significance level, there is sufficient evidence to conclude that the die is not fair.
- [x] At the 5% significance level, there is not enough evidence to conclude that the die is not fair.
Expert Solution

Step 1: Determining the given information
The given test statistic is 4.500 and the critical value is 11.070.
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