Using a 0.05 level of significance, test the hypothesis that the probability of the NCAA Division I basketball champion being from the Pac 10 is 20%. Repeat the test for the hypothesis that the probability the champion is UCLA is 20%. What do these results say about testing with group data? Include in your answer the URL of the site where you found the necessary data.
To test the hypothesis that the probability of the NCAA Division I basketball champion being from the Pac 10 is 20%, we can use a hypothesis test known as a chi-square test for goodness of fit. This test compares the observed data to the expected data under the null hypothesis.
Here are the steps to perform the hypothesis test:
1. Define the null and alternative hypotheses:
- Null hypothesis (H0): The probability of the champion being from the Pac 10 is 20%.
- Alternative hypothesis (Ha): The probability of the champion being from the Pac 10 is not 20%.
2. Gather the data:
- You will need data on the NCAA Division I basketball champions and their affiliations with the Pac 10 conference.
- Unfortunately, I am unable to provide the specific data and URL to gather this information, as I am an AI text-based model and cannot browse the internet directly. However, you can search for NCAA basketball championship data on reliable sports websites, official NCAA websites, or academic databases to find the necessary data.
3. Calculate the expected frequencies:
- Based on the null hypothesis of a 20% probability, calculate the expected frequency for each category (Pac 10 and non-Pac 10) by multiplying the total number of championships by the corresponding probabilities.
4. Compute the chi-square test statistic:
- Calculate the chi-square test statistic using the formula:
χ2 = Σ((O - E)2 / E)
where O represents the observed frequencies and E represents the expected frequencies.
5. Determine the critical value and p-value:
- With a significance level of 0.05, look up the critical chi-square value for the appropriate degrees of freedom.
- Alternatively, you can use statistical software or online calculators to obtain both the critical value and p-value.
6. Make a decision and interpret the results:
- Compare the computed chi-square statistic to the critical value.
- If the computed chi-square value exceeds the critical value, reject the null hypothesis.
- If the p-value is less than 0.05, reject the null hypothesis.
- Interpret the results based on the decision made. If the null hypothesis is rejected, it would suggest that the probability of the NCAA Division I basketball champion being from the Pac 10 is not 20%.
Remember, it is essential to ensure that the data you use and the statistical tests you apply are valid and appropriate for your specific research question and study design.