Demographic study was conducted to verify the age distribution among residents in suburban areas. There were k= 6 age groups selected for this study. The observed frequencies and theoretical proportions under the null hypothesis are shown in the table below. Age Group Under 20 [20, 30) [30, 40) [40, 50) [50, 65) 65 and Above Total Frequency 132 148 224 62 188 46 800

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**Title: Analyzing Age Distribution in Suburban Areas**

A demographic study was conducted to verify the age distribution among residents in suburban areas. The study focused on six age groups. The observed frequencies and theoretical proportions under the null hypothesis are detailed in the table below.

| Age Group     | Under 20 | [20, 30) | [30, 40) | [40, 50) | [50, 65) | 65 and Above | Total |
|---------------|----------|---------|---------|---------|---------|-------------|-------|
| **Frequency** | 132      | 148     | 224     | 62      | 188     | 46          | 800   |
| **Proportions** | 0.15     | 0.20    | 0.25    | 0.10    | 0.25    | 0.05        | 1.00  |
| **EXPECTED**  |          |         |         |         |         |             |       |

### Tasks

1. **Determine Expected Counts:**
   - Calculate the expected frequencies for each age group under the null hypothesis and fill them in the table.
   
2. **Evaluate the Test Statistic:**
   - Use the expected and observed frequencies to calculate the test statistic.

**Solution**

[The solution area is left blank in the image for future computation and elaboration.]
Transcribed Image Text:**Title: Analyzing Age Distribution in Suburban Areas** A demographic study was conducted to verify the age distribution among residents in suburban areas. The study focused on six age groups. The observed frequencies and theoretical proportions under the null hypothesis are detailed in the table below. | Age Group | Under 20 | [20, 30) | [30, 40) | [40, 50) | [50, 65) | 65 and Above | Total | |---------------|----------|---------|---------|---------|---------|-------------|-------| | **Frequency** | 132 | 148 | 224 | 62 | 188 | 46 | 800 | | **Proportions** | 0.15 | 0.20 | 0.25 | 0.10 | 0.25 | 0.05 | 1.00 | | **EXPECTED** | | | | | | | | ### Tasks 1. **Determine Expected Counts:** - Calculate the expected frequencies for each age group under the null hypothesis and fill them in the table. 2. **Evaluate the Test Statistic:** - Use the expected and observed frequencies to calculate the test statistic. **Solution** [The solution area is left blank in the image for future computation and elaboration.]
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