Question
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)
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)
Answers
GPT 3.5
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)
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)