The Pizza Shop wanted to determine what proportion of its customers ordered only cheese pizza. Out of 80 customers surveyed, 15 ordered cheese pizza. They want a 99% confidence interval of the true proportion of customers who order only cheese pizza.
What is the 99% confidence interval of the true proportion of customers who order only cheese pizza?
(0.075, 0.300)
(0.115, 0.260)
(0.086, 0.289)
(0.102, 0.273)
The formula for calculating the confidence interval for a proportion is:
CI = p̂ ± Z * √((p̂ * (1 - p̂)) / n)
Where:
- p̂ is the sample proportion (15/80 = 0.1875),
- Z is the z-score corresponding to the desired confidence level (99% confidence level corresponds to a z-score of approximately 2.576),
- n is the sample size (80).
Using the formula and plugging in the values:
CI = 0.1875 ± 2.576 * √((0.1875 * (1 - 0.1875)) / 80)
CI = 0.1875 ± 2.576 * √((0.14915) / 80)
CI = 0.1875 ± 2.576 * √(0.001864)
CI = 0.1875 ± 2.576 * 0.043163
CI = 0.1875 ± 0.1111354
CI = (0.076, 0.299)
Therefore, the correct answer is: (0.075, 0.300)