Question

A soccer ball manufacturer wants to estimate the mean circumference of soccer balls within 0.1 in (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 in. (b) Repeat part (a) using a population standard deviation of 0.30 in. Which standard deviation requires a larger sample size? Explain 25 a) The minimum sample size required to construct a 99% confidence inte valus (Round up to the nearest integer.) ga ulat n standard deviation of balls. ation fo a n. balls. b) The minimum sample size required to construct a 99% confidence nten al using a population standard de Round up to the nearest integer.) requires a larger sample size. Due othe increased va ability ın he population, a ▼sample size s needed t ensure the desired Apopulation standard deviation o accuracy

Answer 1

Margin of error = 0.1

a) σ = 0.25

Z for 99% confidence interval = Z_0.005 = 2.58

Margin of error = Z_0.005 * σ / sqrt(n)

or, 0.1 = 2.58 * 0.25 / sqrt(n)

or, n = 41.6025

or, n = 42 balls

b) σ = 0.30

Z for 99% confidence interval = Z_0.005 = 2.58

Margin of error = Z_0.005 * σ / sqrt(n)

or, 0.1 = 2.58 * 0.30 / sqrt(n)

or, n = 59.9076

or, n = 60 balls

A population standard deviation of 0.3 in requires a large sample size. Due to increased variability in the population a larger sample size is needed to ensure desire accuracy