Question

Find the margin of error.

The lifetimes (in months) of a set of 50 randomly selected automobile batteries of a particular brand gives a mean of 16 months with a standard deviation of 1.5 months. The manufacturer claims, however, that this particular make of battery has an 18 month lifetime.

Answer 1

To find the margin of error we need confidence level .

Which is not given in the question.

Therefore we use 95% confidence level.

As population standard deviation not given we use t-interval formula to get margin of error.

We have given that : n=50 , s=1.5

c=0.95

Degrees of freedom= n-1 = 50-1 =49

DF= 49

To get the value of tc use Excel function

TINV(probability,deg_freedom)

= TINV( 0.05 , 49 )

= 2.009575

tc = 2.01

Now plug the values in the formula

E = 0.4263853891

Margin of error = 0.426 (rounded to three decimals)