A supplier manufactures rubber baby buggy bumpers for the bu

A supplier manufactures rubber baby buggy bumpers for the bumper cars. A random sample of 500 bumpers is taken and the sample mean life is 10.5 years with a standard deviation of 1.3 years. The law requires 95% confidence of operation when scheduling bumper replacement. What are the lower-limit and the upper-limit of the two-sided confidence interval?

Solution

A supplier manufactures rubber baby buggy bumpers for the bumper cars.

sample size (n) = 500

sample mean (Xbar) = 10.5

standard deviation (s) = 1.3

confidence level (c) = 0.95

Here we use t-interval because information is given regarding sample.

The 95% confidence interval for population mean (mu) is,

Xbar - E < mu < Xbar + E

where E is margin of error.

E = (tc*s) / sqrt(n)

where tc is the critical value for t-distribution. We can find this value by using EXCEL.

syntax :

=TINV(probability, d.f.)

where probability = 1 - c = 1 - 0.95 = 0.05

d.f. = n - 1 = 500 - 1 = 499

tc = 1.9647

E = (1.9647*1.3) / sqrt(500) = 0.1142

lower limit = Xbar - E = 10.5 - 0.1142 = 10.3858

upper limit = Xbar + E = 10.5 + 0.1142 = 10.6142