Name: SOLUTION Statistics 305 Exam 2 part II
June 23rd, 2009
[40 points total]
Problem 1 [16 points total]
In an attempt to investigate the true mean lifetime of a certain brand of 60 watt light bulb, data
were gathered on 30 light bulbs. The data resulted in a sample mean of
1020x
hours and
sample variance of
3600
2
s
hours2.
a) Calculate a two-sided 95% confidence interval for μ, the true mean lifetime of this
type of 60 watt light bulb (and interpret it). [5 pts]
)471.1041,529.998(
30
60
96.11020
96.1025.2/
025.
z
I am 95% confident that the true mean lifetime of this type of 60 watt light bulb is
between 998.529 and 1041.471 hours.
b) What does it mean to be 95% confident? [3 pts]
If I were to take many, many samples of size 30 and compute a 95% confidence interval
for each, I would expect 95% of those intervals to contain the true mean.
c) How big of a sample would I need to take if I wanted to compute a 92% confidence interval
using the same mean and standard deviation above that had a width of 20? [4 pts]
α = .08 so α/2 = 0.04 and zα/2 = 1.75
11125.110
20
)60)(75.1(2
2
n
I would need a sample of 111 light bulbs.
The manufacturer of the 60 watt light bulb claims that the true mean lifetime is 1045 hours. As
part of our study we wish to test whether this claim is true or false.
d) Set up the appropriate null hypothesis and alternative hypothesis. [2 pt]
0
H
: μ = 1045 hours vs.
a
H
: μ ≠ 1045 hours
