Question

A soccer ball manufacturer wants to estimate the mean circumference of soccer balls within 0.1 inch.

(a) Determine the minimum sample size required to construct a 99% confidence interval for the population mean. Assume the population standard deviation is 0.25 inch.
(b) Repeat part (a) using a population standard deviation of 0.3 inch.
(c) Which standard deviation requires a larger sample size

Answer 1

Explanation:

Given that a soccer ball manufacturer wants to estimate the mean circumference of soccer balls within 0.1 inch.

a) sigma = 0.25

Since population std dev is known we can use Z critical value i.e. 2.58

`2.58(\sigma/√(n) )<0.1\\√(n) >25.8*\sigma\\i.e. n>665.64 \sigma^2`

Hence when sigma =0.25

we get n should be atleast = 41.6025 or 42

b) when sigma = 0.3 we get

n >59.390=60

c) Big std deviation requires larger sample size.