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 σ = .000996 mm. Assume a random sample of 59 sheets of metal resulted in an x¯ = .2266 mm. Calculate the 98 percent confidence interval for the true mean metal thickness. (Round your answers to 4 decimal places.) The 98% confidence interval is from to

Answer 1

Given that,

= 0.2266

= 0.000996

n = 59

At 98% confidence level the z is ,

  = 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02/ 2 = 0.01

Z_/2 = Z_0.01 = 2.326

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

= 2.326 * ( 0.000996/ 59)

= 0.0003

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

- E < < + E

0.2266 - 0.0003 < < 0.2266 + 0.0003

0.2263< <0.2269

(0.2263,0.2269 )