Question

a pizza shop owner wishes to find the 95% confidence interval of the true mean cost of a large plain pizza. How large should the sample be if she wishes to accurate to within $0.15?

Answer 1

To find the sample size needed to estimate the true mean cost of a large plain pizza with a 95% confidence interval and an accuracy of $0.15, you can use the formula n = (Z * σ) / E. Since we don't have the population standard deviation, we can use a sample standard deviation as an approximation.

Step-by-step explanation:

To find the sample size needed to estimate the true mean cost of a large plain pizza with a 95% confidence interval and an accuracy of $0.15, we can use the formula:

n = (Z * σ) / E

Where:

• n is the required sample size
• Z is the Z-value corresponding to the desired confidence level (for 95% confidence, Z ≈ 1.96)
• σ is the population standard deviation
• E is the desired margin of error (accuracy)

Since we don't have the population standard deviation, we can use a sample standard deviation as an approximation. Given that the population standard deviation is usually unknown, a sample size of at least 30 is generally considered sufficient.