To create a confidence interval for the percentage of people who may buy something based on the given information, we can use the following formula:
CI = p̂ ± Z * √(p̂ * (1-p̂) / n)
where:
- p̂ is the sample proportion (the number of orders divided by the total number of people contacted)
- Z is the Z-score corresponding to the desired confidence level (90% in this case)
- n is the sample size (the number of people contacted)
First, we calculate the sample proportion:
p̂ = (number of orders) / (total number of people contacted)
= 148 / 1180
≈ 0.1254
Next, we need to find the Z-score corresponding to a 90% confidence level. We can use a standard normal distribution table or a statistical calculator. For a 90% confidence level, the Z-score is approximately 1.645.
Now we can plug the values into the formula to calculate the confidence interval:
CI = 0.1254 ± 1.645 * √(0.1254 * (1-0.1254) / 1180)
Calculating the values inside the square root:
√(0.1254 * (1-0.1254) / 1180) ≈ 0.0139
Plugging back into the formula:
CI = 0.1254 ± 1.645 * 0.0139
Calculating the values:
CI = 0.1254 ± 0.0229
Therefore, the 90% confidence interval for the percentage of people the company contacts who may buy something is approximately:
0.1025 ≤ p ≤ 0.1483
This means that we can be 90% confident that the true percentage of people who may buy something lies within the range of 10.25% to 14.83%.