A soccer ball manufactuirer wants to estimate the mean circumference of soccer b

Question

A soccer ball manufactuirer wants to estimate the mean circumference of soccer balls within 0.05 in (a Determine the mm r um sample sze re u red to construct a 9% con dereen erval f r the population mean. Assume the da on standard dena on s (b) Repeat part (a) using a population standard deviation of 0.35 in. Which standard deviation requires a larger sample size? Explain (a)The minimum sample size reored to construct a 9g% confidence interval using a population standard deviation of 25 in is bans (Round up to the nearest integer b The mi nmum sar ke sze requred to construct a99% confido conter a usrg a po ulation standard deviation of 35in. bas Round up to the nearest integer) 25 sample size is needed to ensure A population standard deviation of the desired accuracy. in requires a larger sample size Due to the increased variablity in the population, a 0 36 025 Enter your answer in each of the

Explanation / Answer

(a)  E = 0.05 , where E = margin of error,

s.d. = ? = 0.25
s.e. = ? / ?n = 0.25 / ?n
Z? = 2.58 at 99% confidence.
also, E = s.e.× Z? = 0.05
=> 0.25 × 2.58 / ?n = 0.05
=> ?n = 0.25 × 2.58/ 0.05 = 12.9
=> n = 167 (approx.)

(b) E = 0.05 , where E = margin of error,

s.d. = ? = 0.35
s.e. = ? / ?n = 0.35 / ?n
Z? = 2.58 at 99% confidence.
also, E = s.e.× Z? = 0.05
=> 0.35 × 2.58 / ?n = 0.05
=> ?n = 0.35 × 2.58/ 0.05 = 18.06
=> n = 327 (approx.)

Standard Deviation 0.35 requires a larger sample size

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