Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Get quick and reliable solutions to your questions from knowledgeable professionals on our comprehensive Q&A platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
To solve this problem, we need to determine whether we should reject or not reject the null hypothesis [tex]\( H_0 \)[/tex] based on the chi-square Goodness-of-Fit test results.
1. Restate the hypotheses:
- Null hypothesis ([tex]\( H_0 \)[/tex]): The die has a uniform distribution.
- Alternative hypothesis ([tex]\( H_a \)[/tex]): The die does not have a uniform distribution.
2. Given information:
- Calculated chi-square value ([tex]\( \chi^2 \)[/tex] or [tex]\( \chi_0^2 \)[/tex]): 11.692
- Critical chi-square value at 1% significance level ([tex]\( \chi_{0.01}^2 \)[/tex]): 15.086
- Significance level ([tex]\( \alpha \)[/tex]): 0.01 (or 1%)
3. Decision rule for the chi-square test:
- If the calculated chi-square value is greater than the critical chi-square value, we reject [tex]\( H_0 \)[/tex].
- If the calculated chi-square value is less than or equal to the critical chi-square value, we do not reject [tex]\( H_0 \)[/tex].
4. Compare the calculated chi-square value to the critical chi-square value:
- Calculated chi-square value: 11.692
- Critical chi-square value: 15.086
5. Make the decision:
- Since the calculated chi-square value (11.692) is less than the critical chi-square value (15.086), we do not reject the null hypothesis [tex]\( H_0 \)[/tex].
6. Conclusion:
- We should not reject [tex]\( H_0 \)[/tex].
Therefore, the conclusions that can be drawn are:
- We should not reject [tex]\( H_0 \)[/tex].
1. Restate the hypotheses:
- Null hypothesis ([tex]\( H_0 \)[/tex]): The die has a uniform distribution.
- Alternative hypothesis ([tex]\( H_a \)[/tex]): The die does not have a uniform distribution.
2. Given information:
- Calculated chi-square value ([tex]\( \chi^2 \)[/tex] or [tex]\( \chi_0^2 \)[/tex]): 11.692
- Critical chi-square value at 1% significance level ([tex]\( \chi_{0.01}^2 \)[/tex]): 15.086
- Significance level ([tex]\( \alpha \)[/tex]): 0.01 (or 1%)
3. Decision rule for the chi-square test:
- If the calculated chi-square value is greater than the critical chi-square value, we reject [tex]\( H_0 \)[/tex].
- If the calculated chi-square value is less than or equal to the critical chi-square value, we do not reject [tex]\( H_0 \)[/tex].
4. Compare the calculated chi-square value to the critical chi-square value:
- Calculated chi-square value: 11.692
- Critical chi-square value: 15.086
5. Make the decision:
- Since the calculated chi-square value (11.692) is less than the critical chi-square value (15.086), we do not reject the null hypothesis [tex]\( H_0 \)[/tex].
6. Conclusion:
- We should not reject [tex]\( H_0 \)[/tex].
Therefore, the conclusions that can be drawn are:
- We should not reject [tex]\( H_0 \)[/tex].
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We hope this was helpful. Please come back whenever you need more information or answers to your queries. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.