A preliminary study regarding the number of AIDS cases reported for Santa Clara County, California is broken down by race in the table below. White Hispanic Black Race Asian/Pacific Islander Total Cases 25 11 9 3 48 Conduct a chi-square test for goodness-of-fit to determine whether or not the occurrence of AIDS cases is consistent with the race distribution of Santa Clara County. Choose the correct pull and alternative hypotheses

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**A Preliminary Study on AIDS Cases in Santa Clara County, California**

**Race Distribution of AIDS Cases:**
- **White:** 25 cases
- **Hispanic:** 11 cases
- **Black:** 9 cases
- **Asian/Pacific Islander:** 3 cases
- **Total:** 48 cases

**Objective:**
Conduct a chi-square test for goodness-of-fit to determine if the occurrence of AIDS cases is consistent with the race distribution of Santa Clara County.

**Hypotheses:**
- **\( H_0 \):** The distribution of AIDS cases is consistent with the race distribution in Santa Clara County.
- **\( H_a \):** The distribution of AIDS cases is different from the race distribution in Santa Clara County.

**Population Distribution in Santa Clara County (Proportion and Expected Cases):**
- **White:**
  - Proportion: 0.409
  - Expected Cases: (To be calculated)
- **Hispanic:**
  - Proportion: 0.273
  - Expected Cases: (To be calculated)
- **Black:**
  - Proportion: 0.027
  - Expected Cases: (To be calculated)
- **Asian/Pacific Islander:**
  - Proportion: 0.291
  - Expected Cases: (To be calculated)
- **Total:**
  - Proportion: 1
  - Expected Cases: (Sum should equal 48)

**Question:**
Calculate the test statistic using the chi-square formula, and evaluate the consistency between the observed and expected distributions.
Transcribed Image Text:**A Preliminary Study on AIDS Cases in Santa Clara County, California** **Race Distribution of AIDS Cases:** - **White:** 25 cases - **Hispanic:** 11 cases - **Black:** 9 cases - **Asian/Pacific Islander:** 3 cases - **Total:** 48 cases **Objective:** Conduct a chi-square test for goodness-of-fit to determine if the occurrence of AIDS cases is consistent with the race distribution of Santa Clara County. **Hypotheses:** - **\( H_0 \):** The distribution of AIDS cases is consistent with the race distribution in Santa Clara County. - **\( H_a \):** The distribution of AIDS cases is different from the race distribution in Santa Clara County. **Population Distribution in Santa Clara County (Proportion and Expected Cases):** - **White:** - Proportion: 0.409 - Expected Cases: (To be calculated) - **Hispanic:** - Proportion: 0.273 - Expected Cases: (To be calculated) - **Black:** - Proportion: 0.027 - Expected Cases: (To be calculated) - **Asian/Pacific Islander:** - Proportion: 0.291 - Expected Cases: (To be calculated) - **Total:** - Proportion: 1 - Expected Cases: (Sum should equal 48) **Question:** Calculate the test statistic using the chi-square formula, and evaluate the consistency between the observed and expected distributions.
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