To create a confidence interval for the percentage of people who may buy something, we can use the formula for estimating a population proportion.
The formula for calculating the confidence interval for a proportion is:
CI = p̂ ± Z * √(p̂(1 - p̂) / n)
Where:
CI is the confidence interval
p̂ is the sample proportion (in this case, the proportion of recipients who placed an order)
Z is the Z-score (corresponding to the desired confidence level)
n is the sample size (the number of people who received the flyer)
In this scenario, the sample proportion p̂ is calculated as the number of recipients who placed an order divided by the total number of recipients: p̂ = 114/1150 = 0.0991.
To determine the Z-score, we need to specify the desired confidence level. Since the question asks for a 90% confidence interval, the corresponding Z-score for a two-tailed test is 1.645. This value can be obtained from a standard normal distribution table or calculated using statistical software.
Now, we can plug in the values into the formula to calculate the confidence interval:
CI = 0.0991 ± 1.645 * √((0.0991 * (1 - 0.0991)) / 1150)
Calculating the expression inside the square root:
√((0.0991 * (1 - 0.0991)) / 1150) ≈ 0.0098
Substituting this value into the formula:
CI = 0.0991 ± 1.645 * 0.0098
Calculating the values:
CI = 0.0991 ± 0.0161
This gives us the confidence interval:
CI ≈ (0.0829, 0.1153)
Therefore, at a 90% confidence level, we can estimate that the percentage of people the company contacts who may buy something is between approximately 8.29% and 11.53%.