The manager of a pizza chain in Albuquerque, New Mexico, wants to determine the
ID: 3152945 • Letter: T
Question
The manager of a pizza chain in Albuquerque, New Mexico, wants to determine the average size of their advertised 13-inch pizzas. She takes a random sample of 37 pizzas and records their mean and standard deviation as 13.50 and 1.90 inches, respectively. She subsequently computes a 95% confidence interval of the mean size of all pizzas as [12.89, 14.11]. However, she finds this interval to be too broad to implement quality control and decides to reestimate the mean based on a bigger sample. Using the standard deviation estimate of 1.90 from her earlier analysis, how large a sample must she take if she wants the margin of error to be under 0.5 inch? Use Table 1. (Round intermediate calculations to 4 decimal places and "z" value to 2 decimal places. Round up your answer to the nearest whole number.)
Explanation / Answer
the z score foe 95% = 1.96
the margin of error = 0.5
the standard deviation = 1.9
the formula for margin of error = zscore*standard deviation/sqrt(n)
therefore accoding to the formula
0.5 = 1.96*1.9/sqrt(n)
squaring both sides
n = (1.96*1.9/0.5)^2 = 55.47 = 55
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