Question

A soccer ball manufacturer wants to estimate the mean circumference of soccer balls within 0.05 in.

Answer 1

Answer:

107,426, bigger

Step-by-step explanation:

Given that a soccer ball manufacturer wants to estimate the mean circumference of soccer balls within 0.05 in.

Margin of error = 0.05 inches

Since population std deviation is known we can use z critical value.

(a) i.e. for 99% confidence interval

Z critical = 2.58

$2.58(\frac{0.20}{\sqrt{n} } )106.50\\n>107$

A minimum sample size of 107 needed.

b) $2.58(\frac{0.40}{\sqrt{n} } )426$

Here minimum sample size = 426

Due to the increased variability in the population, a bigger sample size is needed to ensure the desired accuracy.