Question

The Ball Corporation's beverage can manufacturing plant in Fort Atkinson, Wisconsin, uses a metal supplier that provides metal with a known thickness standard deviation a=.000672 mm. Assume a random sample of 56 sheets of metal resulted in an x=.2737 mm

Calculate the 98 percent confidence interval for the true mean metal thickness

Interval is from ? to ? Round to 4 decimal places

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 0.2737

Population standard deviation = = 0.000672

Sample size = n = 56

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

Z/2 = Z0.01 = 2.326

Margin of error = E = Z/2* ( /n)

= 2.326 * (0.000672 / 56 )

= 0.0002

At 98% confidence interval estimate of the population mean is,

- E < < + E

0.2737 - 0.0002 < <0.2737 + 0.0002

0.2735 < < 0.2739

( , )