Historically, the proportion of adults over the age of 24 who smoke has been estimated to be .30. You want to take a sample to estimate the current proportion of adults over the age of 24 who smoke within 3% at 95% accuracy. When you completed the sample you found that 114 of those adults sampled over the age of 24 smoked. Develop a 95% confidence interval for the current proportion of adults over the age of 24 who smoke.

To develop a 95% confidence interval for the current proportion of adults over the age of 24 who smoke, we can use the sample data. Let's break down the steps to calculate the confidence interval using the given information:

Step 1: Determine the sample proportion
The sample proportion is calculated by dividing the number of adults over the age of 24 who smoke (114) by the sample size.

Sample Proportion (p̂) = Number of adults over 24 who smoke / Sample Size

p̂ = 114 / Sample Size

Step 2: Determine the standard error
The standard error measures the variability of the sample proportion. It is calculated using the formula:

Standard Error (SE) = sqrt[(p̂ * (1 - p̂)) / Sample Size]

Step 3: Determine the critical value
The critical value corresponds to a chosen confidence level and sample size. For a 95% confidence level, the critical value is approximately 1.96.

Step 4: Calculate the margin of error
The margin of error is the maximum distance between the sample proportion and the confidence interval boundaries. It is calculated by multiplying the standard error by the critical value.

Margin of Error = Critical Value * Standard Error

Step 5: Calculate the lower and upper bounds of the confidence interval
To calculate the lower and upper bounds, we subtract and add the margin of error from the sample proportion.

Lower Bound = Sample Proportion - Margin of Error
Upper Bound = Sample Proportion + Margin of Error

Now, let's put it all together and calculate the confidence interval:

Given: Sample Proportion (p̂) = 114 / Sample Size, Sample Size, Confidence Level (95%)

1. Determine the sample proportion:
p̂ = 114 / Sample Size

2. Determine the standard error:
SE = sqrt[(p̂ * (1 - p̂)) / Sample Size]

3. Determine the critical value:
Critical Value = 1.96 (for a 95% confidence level)

4. Calculate the margin of error:
Margin of Error = Critical Value * Standard Error

5. Calculate the lower and upper bounds:
Lower Bound = Sample Proportion - Margin of Error
Upper Bound = Sample Proportion + Margin of Error

Substitute the variables with the given values, and solve for the confidence interval.