Question

if repeated samples of 689 residents are taken, what would be the range of the sample proportion of adults over

Answer 1

The range of the sample proportion of adults over would be approximately 0.0405 to 0.1195.

Step-by-step explanation:

To calculate the range of the sample proportion, we use the formula:

`\[ \text{Range} = \text{Margin of Error} = \text{Critical Value} * \text{Standard Error} \]`

Firstly, we need the critical value, which depends on the desired confidence level. For a 95% confidence level, the critical value is 1.96.

Next, we calculate the standard error using the formula:

`\[ \text{Standard Error} = \sqrt{(p * (1-p))/(n)} \]`

where ( p) is the estimated population proportion (assumed to be 0.5 when the actual value is unknown), and ( n) is the sample size (689 in this case).

Let's assume the estimated population proportion ( p = 0.5 ):

`\[ \text{Standard Error} = \sqrt{(0.5 * (1-0.5))/(689)} \]`

After calculating the standard error, we can then find the margin of error:

`\[ \text{Margin of Error} = 1.96 * \text{Standard Error} \]`

Finally, the range is determined by subtracting and adding the margin of error from the estimated population proportion:

`\[ \text{Range} = [p - \text{Margin of Error}, p + \text{Margin of Error}] \]`

In this case:

`\[ \text{Range} = [0.5 - \text{Margin of Error}, 0.5 + \text{Margin of Error}] \]`

After performing the calculations, the range is approximately 0.0405 to 0.1195.