A soccer ball manufacturer wants to estimate the mean circumference of soccer balls within 0.05 in. (a) Determine the minimum sample size required to construct a 99% confidence interval for the population mean. Assume the population standard deviation is 0.20 in. (b) Repeat part (a) using a standard deviation of 0.40 in. Which standard deviation requires a larger sample size? Explain. (a) The minimum sample size required to construct a 99% confidence interval using a population standard deviation of 0.20 in. is balls. (Round up to the nearest integer.) (b) The minimum sample size required to construct a 99% confidence interval using a standard deviation of 0.40 in. is balls. (Round up to the nearest integer.) A population standard deviation of in. requires a larger sample size. Due to the increased variability in the population, a sample size is needed to ensure the desired accuracy.

Question
Answer:
Answer:107,426, biggerStep-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 inchesSince population std deviation is known we can use z critical value.(a) i.e. for 99% confidence intervalZ critical = 2.58[tex]2.58(\frac{0.20}{\sqrt{n} } )<0.05\\n>106.50\\n>107[/tex]A minimum sample size of 107 needed.b) [tex]2.58(\frac{0.40}{\sqrt{n} } )<0.05\\\\\\n>426[/tex]Here minimum sample size = 426Due to the increased variability in the population, a bigger sample size is needed to ensure the desired accuracy.
solved
general 10 months ago 4362