Question

A company manufacturing stereo equipment claims that their personal CD player can be used
for approximately 8 hours of continuous play when used with alkaline batteries. To provide this
estimate, the company tested 35 CD players with new alkaline batteries and recorded the time
at which the batteries in the players “lost power”. The average time was 8.3 hours with a
sample standard deviation of 1.2 hours.
(a) Construct a 98% confidence interval for the mean time until a new alkaline battery used
in the CD player loses power.
(b) Determine the required sample size in order to estimate the mean time until a new
alkaline battery used in the CD player loses power to within ±10 minutes at the 99%
confidence level.

Answer 1

(a)

n = 35

= 8.3

s = 1.2

= 0.02

df= 35 - 1 = 34

From Table, critical values of t = 2.441

Confidence Interval:

So,

Answer is:
(7.805, 8.795)

(b)

Sample Size (n) is given by:

Given:

= 0.01

From Table, critical values of Z = 2.576

= 1,2

e = 10/60 = 0.1667

Substituting, we get:

So,

Answer is:

344