Question

The following data represent the battery life, in hours, for a random sample of ten full charges on iPod music player.

7.3

10.2

12.9

10.8

12.1

6.6

10.2

9.0

8.5

7.1

(a) Construct a 90% confidence interval for the mean number of hours the battery will last on this player.

(b) Suppose you wanted more accuracy. What can be done to increase the accuracy of the interval without changing the level of confidence?

Answer 1

ANSWER:
a)

Confidence Interval
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=9.47
Standard deviation( sd )=2.146
Sample Size(n)=10
Confidence Interval = [ 9.47 ± t a/2 ( 2.146/ Sqrt ( 10) ) ]
= [ 9.47 - 1.8331 * (0.68) , 9.47 + 1.8331 * (0.68) ]
= [ 8.23,10.71 ]

b)

increase the size of the interval