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 28 19 6 Race 3 56 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 null and alternative hypotheses: O Ho: The distribution of AIDS cases is different from the race distribution in Santa Clara County. Ha: The distribution of AIDS cases is consistent with the race distribution in Santa Clara County. Ho: The distribution of AIDS cases is consistent with the race distribution in Santa Clara County. Ha: The distribution of AIDS cases is different from the race distribution in Santa Clara County. The population distribution of Santa Clara County by race is provided in the table below. Use these percentages to compute the expected number of cases for each racial group. Round your answers to three decimal places, if necessary. Part 2 o Proportion Expected cases

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### Study on AIDS Cases by Race in Santa Clara County, California

#### Reported Cases Breakdown

The table below presents the number of AIDS cases reported in Santa Clara County, categorized by race:

| Race                  | Cases |
|-----------------------|-------|
| White                 | 28    |
| Hispanic              | 19    |
| Black                 | 6     |
| Asian/Pacific Islander| 3     |
| **Total**             | **56**|

#### Chi-Square Test for Goodness-of-Fit

We aim to determine if the racial distribution of these AIDS cases aligns with the overall racial distribution in Santa Clara County.

**Formulate Hypotheses:**

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

The correct null hypothesis, as indicated, is:

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

#### Population Distribution by Race

To calculate the expected number of AIDS cases for each racial group, use the population distribution of Santa Clara County:

| Race                  | Proportion | Expected Cases (Fill in) |
|-----------------------|------------|--------------------------|
| White                 | 0.441      |                          |
| Hispanic              | 0.25       |                          |
| Black                 | 0.028      |                          |
| Asian/Pacific Islander| 0.281      |                          |
| **Total**             | **1**      |                          |

Use these proportions to compute expected cases, rounding your answers to three decimal places if necessary.
Transcribed Image Text:### Study on AIDS Cases by Race in Santa Clara County, California #### Reported Cases Breakdown The table below presents the number of AIDS cases reported in Santa Clara County, categorized by race: | Race | Cases | |-----------------------|-------| | White | 28 | | Hispanic | 19 | | Black | 6 | | Asian/Pacific Islander| 3 | | **Total** | **56**| #### Chi-Square Test for Goodness-of-Fit We aim to determine if the racial distribution of these AIDS cases aligns with the overall racial distribution in Santa Clara County. **Formulate Hypotheses:** - Null Hypothesis (\(H_0\)): The distribution of AIDS cases is consistent with the race distribution in Santa Clara County. - Alternative Hypothesis (\(H_a\)): The distribution of AIDS cases is different from the race distribution in Santa Clara County. The correct null hypothesis, as indicated, is: - \(H_0\): The distribution of AIDS cases is consistent with the race distribution in Santa Clara County. #### Population Distribution by Race To calculate the expected number of AIDS cases for each racial group, use the population distribution of Santa Clara County: | Race | Proportion | Expected Cases (Fill in) | |-----------------------|------------|--------------------------| | White | 0.441 | | | Hispanic | 0.25 | | | Black | 0.028 | | | Asian/Pacific Islander| 0.281 | | | **Total** | **1** | | Use these proportions to compute expected cases, rounding your answers to three decimal places if necessary.
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