Question

A supplier manufactures rubber baby buggy bumpers for the bumper cars. A random sample of 256 bumpers is taken and the sample mean life is 3.5 years with a standard deviation of .5 years. The law requires 95% confidence of operation when scheduling bumper replacement. What are: a) the lower-limit [A] and b) the upper-limit [B] of the two-sided confidence interval?

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 3.5

sample standard deviation = s = 0.5

sample size = n = 256

Degrees of freedom = df = n - 1 = 256 -1 = 255

At 95% confidence level

= 1-0.95% =1-0.95 =0.05

/2 =0.05/ 2= 0.025

t/2,df = t0.025,255= 1.97

t /2,df = 1.97

Margin of error = E = t/2,df * (s /n)

= 1.97 * ( 0.5 / 256)

Margin of error = E = 0.062

The 95% confidence interval estimate of the population mean is,

- E < <  + E

3.5 + 0.062 < < 3.5 +0.062

3.438 < < 3.562

(3.438,3.562)

lower limit = 3.438

Upper limit = 3.562