Question

1. ) A soccer ball manufacturer wants to estimate the mean circumference of soccer balls within 0.15 inch.

1. Determine the minimum sample size required to construct a 99% confidence interval for the population mean. Assume that the population standard deviation is 0.5 inch.   

2. The sample mean is 27.5 inches. With a sample size of if 84, a 99% level of confidence, and a population standard deviation of 0.5inch, does it seem possible that the population mean could be less than 27.6 inches? Explain.

Answer 1

Answer)

As the population s.d is known here, so we can use standard normal z table to estimate the answers.

A)

Critical value z from z table for 99% confidence level is 2.576

Margin of error (MOE) = z*s.d/√n

0.15 = 2.576*0.15/√n

N = 74.

B)

Null hypothesis Ho : u = 27.6

Alternate hypothesis Ha : u < 27.6

Margin of error (MOE) = z*s.d/√n = 2.576*0.5/√84 = 0.14053232131

Interval is given by,

(Mean - MOE, Mean + MOE).

(27.3594676786, 27.6405323213)

As the interval contain the null hypothesised value 27.6 in it.

We fail to reject the null hypothesis Ho.

So, we do not have enough evidence to conclude that the population mean could be less than 27.6 inches.