Refer to the following scenario. A government official is in charge of allocating social programs throughout the city of Vancouver. He will decide where these social outreach programs should be located based on the percentage of residents living below the poverty line in each region of the city. He takes a simple random sample of 123 people living in Gastown and finds that 23 have an annual income that is below the poverty line. Suppose that the government official wants to re-estimate the population proportion and wishes for his 90% confidence interval to have a margin of error no larger than 0.03. How large a sample should he take to achieve this? Please carry answers to at least six decimal places in intermediate steps, and use at least 3 decimal places in your critical value. Sample size =

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### Scenario for Statistical Analysis

A government official is responsible for allocating social programs throughout the city of Vancouver. The allocation is based on the percentage of residents living below the poverty line in each city region. For this analysis, the official takes a simple random sample of 123 people from Gastown and discovers that 23 have an annual income below the poverty line.

The aim is to re-estimate the population proportion, ensuring that the 90% confidence interval has a margin of error no larger than 0.03. To achieve this, it's important to determine the necessary sample size. Please ensure calculations carry to at least six decimal places in intermediate steps and that the critical value is expressed with at least three decimal places.

**Sample size =**
Transcribed Image Text:### Scenario for Statistical Analysis A government official is responsible for allocating social programs throughout the city of Vancouver. The allocation is based on the percentage of residents living below the poverty line in each city region. For this analysis, the official takes a simple random sample of 123 people from Gastown and discovers that 23 have an annual income below the poverty line. The aim is to re-estimate the population proportion, ensuring that the 90% confidence interval has a margin of error no larger than 0.03. To achieve this, it's important to determine the necessary sample size. Please ensure calculations carry to at least six decimal places in intermediate steps and that the critical value is expressed with at least three decimal places. **Sample size =**
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