Question

Efficient manufacturing:(please make answer clear ) Efficiency experts study the processes used to manufacture items in order to make them as efficient as possible. One of the steps used to manufacture a metal clamp involves the drilling of three holes. In a sample of 75 clamps, the mean time to complete this step was 41.4 seconds. Assume that the population standard deviation is =σ  12 seconds. Round the critical value to no less than three decimal places.

(b) Find the sample size needed so that a 99.5% confidence interval will have margin of error of 1.5

A sample size of ___ is needed in order to obtain a 99.5% confidence interval with a margin error of 1.5 . Round the sample size up to the nearest integer

1.5

Answer 1

 

A) Point estimate = sample mean = = 41.4

Population standard deviation =    = 12

Sample size = n = 75

At 99.5% confidence level the z is,

= 1 - 99.5%

= 1 - 0.995 = 0.005

/2 = 0.0025

Z/2 = Z0.0025 = 2.807

Margin of error = E = Z/2 * ( /√￣n)

E = 2.807 * (12 /  √￣ 75)

E = 3.889

B) Margin of error = E = 1.5

At 99.5% confidence level the z is,

= 1 - 99.5%

= 1 - 0.995 = 0.005

/2 = 0.0025

Z/2 = Z0.0025 = 2.807

sample size = n = [Z/2* / E] 2

n = [2.807 * 12 / 1.5]2

n = 504.27

Sample size = n = 505