In: Statistics and Probability
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.
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