Question

A soccer ball manufacturer wants to estimate the mean circumference of soccer balls within 0.14 inch.

(a) Determine the minimum sample size required to construct a 99​% confidence interval for the population mean. Assume the population standard deviation is 0.7 inch.

​(b) The sample mean is 27.2 inches. With a sample size of 175​, a 99​% level of​ confidence, and a population standard deviation of 0.7 ​inch, does it seem possible that the population mean could be less than 27.3 ​inches? Explain.

​(a) The minimum sample size required to construct a 99​% confidence interval is __ nothing soccer balls.

​(Round up to the nearest whole​ number.)

Answer 1

a)

Sample size = (Z/2 * / E)²

= ( 2.5758 * 0.7 / 0.14)²

= 165.9

Sample size = 166 (Rounded up to nearest integer)

b)

H0: >= 27.3

Ha: < 27.3

Test statistics

z = ( - ) / ( / sqrt(n) )

= ( 27.2 - 27.3) / (0.7 / sqrt(175)

= -1.89

Critical value at 0.01 significance level = -2.326

Since test statistics > -2.326, fail to reject H0.

We conclude at 0.01 significance level, we fail to support the claim that the population mean could be less

than 27.3 ​inches.