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 be accurate to within $0.14 ? A previous study showed that the standard deviation of the price was $0.40. Round your final answer up to the next whole number.

Answer 1

Given that Margin of error = $0.14

Given Standard Deviation = $0.4

Given Confidence level = 95% = 0.95

= 1 - confidence level

= 1 - 0.95

= 0.05

/2 = 0.025

Z_/2 will be z-score that has an area of 0.025 to its right or 0.975 to its left

Z_/2 = 1.96 from the below attached table

Margin of error = Z_/2 * ( / )

Where n is the sample size

0.14 = 1.96 * (0.4 / )

= (1.96 * 0.4) / 0.14

= 0.784 / 0.14

= 5.6

squaring on both sides we have

()² = 5.6²

n = 31.36

So n = 32 rounded up to the next whole number