Welcome to Westonci.ca, your go-to destination for finding answers to all your questions. Join our expert community today! Get detailed and accurate answers to your questions from a community of experts on our comprehensive Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
To determine the null and alternative hypotheses for this chi-square Goodness-of-Fit test, let’s first understand what the test aims to accomplish.
The chi-square Goodness-of-Fit test is used to determine if a sample data fits a population with a specific distribution. In this context, we are testing whether a die has a uniform distribution, which means each outcome (1 through 6) should be equally likely.
Step-by-Step Solution:
1. Understand the Null Hypothesis ([tex]\(H_0\)[/tex]):
- The null hypothesis ([tex]\(H_0\)[/tex]) represents the idea that there is no difference between the observed and expected frequencies. In other words, any deviations from the expected frequencies are due to random chance.
- In this case, [tex]\(H_0\)[/tex] would state that the die is fair and follows a uniform distribution. This means that the probability of rolling any number from 1 to 6 is the same (i.e., [tex]\(\frac{1}{6}\)[/tex] for a fair die).
2. Formulate the Null Hypothesis ([tex]\(H_0\)[/tex]):
- [tex]\(H_0\)[/tex]: The die has the uniform distribution.
3. Understand the Alternative Hypothesis ([tex]\(H_a\)[/tex]):
- The alternative hypothesis ([tex]\(H_a\)[/tex]) represents the idea that there is a significant difference between the observed and expected frequencies. This signifies that the observed deviations are not due to random chance, suggesting the die does not follow a uniform distribution.
- In this scenario, [tex]\(H_a\)[/tex] would state that the die is not fair and does not follow a uniform distribution. This means the probabilities of rolling the numbers from 1 to 6 are not equal.
4. Formulate the Alternative Hypothesis ([tex]\(H_a\)[/tex]):
- [tex]\(H_a\)[/tex]: The die does not have the uniform distribution.
Therefore, the correct hypotheses for this test are:
- [tex]\(H_0\)[/tex]: The die has the uniform distribution.
- [tex]\(H_a\)[/tex]: The die does not have the uniform distribution.
Select the correct null and alternative hypotheses from the given options:
- [tex]\(H_0\)[/tex]: The die has the uniform distribution. (Correct)
- [tex]\(H_a\)[/tex]: The die has the uniform distribution. (Incorrect)
- [tex]\(H_0\)[/tex]: The die does not have the uniform distribution. (Incorrect)
- [tex]\(H_a\)[/tex]: The die does not have the uniform distribution. (Correct)
The chi-square Goodness-of-Fit test is used to determine if a sample data fits a population with a specific distribution. In this context, we are testing whether a die has a uniform distribution, which means each outcome (1 through 6) should be equally likely.
Step-by-Step Solution:
1. Understand the Null Hypothesis ([tex]\(H_0\)[/tex]):
- The null hypothesis ([tex]\(H_0\)[/tex]) represents the idea that there is no difference between the observed and expected frequencies. In other words, any deviations from the expected frequencies are due to random chance.
- In this case, [tex]\(H_0\)[/tex] would state that the die is fair and follows a uniform distribution. This means that the probability of rolling any number from 1 to 6 is the same (i.e., [tex]\(\frac{1}{6}\)[/tex] for a fair die).
2. Formulate the Null Hypothesis ([tex]\(H_0\)[/tex]):
- [tex]\(H_0\)[/tex]: The die has the uniform distribution.
3. Understand the Alternative Hypothesis ([tex]\(H_a\)[/tex]):
- The alternative hypothesis ([tex]\(H_a\)[/tex]) represents the idea that there is a significant difference between the observed and expected frequencies. This signifies that the observed deviations are not due to random chance, suggesting the die does not follow a uniform distribution.
- In this scenario, [tex]\(H_a\)[/tex] would state that the die is not fair and does not follow a uniform distribution. This means the probabilities of rolling the numbers from 1 to 6 are not equal.
4. Formulate the Alternative Hypothesis ([tex]\(H_a\)[/tex]):
- [tex]\(H_a\)[/tex]: The die does not have the uniform distribution.
Therefore, the correct hypotheses for this test are:
- [tex]\(H_0\)[/tex]: The die has the uniform distribution.
- [tex]\(H_a\)[/tex]: The die does not have the uniform distribution.
Select the correct null and alternative hypotheses from the given options:
- [tex]\(H_0\)[/tex]: The die has the uniform distribution. (Correct)
- [tex]\(H_a\)[/tex]: The die has the uniform distribution. (Incorrect)
- [tex]\(H_0\)[/tex]: The die does not have the uniform distribution. (Incorrect)
- [tex]\(H_a\)[/tex]: The die does not have the uniform distribution. (Correct)
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.
