Interval Estimation

Homework 9. Interval EstimationDue Thursday, 11/10, by 11 am
(1) A study of two kinds of photocopying equipment shows that 61 failures of
the first kind of equipment took on the average 80.7 minutes to repair with
a standard deviation of 19.4 minutes, whereas 61 failures of the second kind
of equipment took on the average 88.1 minutes to repair with a standard
deviation of 18.8 minutes. Find a 99% confidence interval for the difference
between the true average amounts of time it takes to repair failures of the
two kinds of photocopying equipment.
(2) Twenty pilots were tested in a flight simulator, and the time for each to
complete a certain corrective action was measured in seconds, with the
following results:
5.2
5.6
7.6
6.8
4.8
5.7
9.0
6.0
4.9
7.4
6.5
7.9
6.8
4.3
8.5
3.6
6.1
5.8
6.4
4.0
Use a computer program to find a 95% confidence interval for the mean
time to take corrective action.
(3) If x is a value of a random variable having an exponential distribution
with parameter θ (probability density function is θ1 e−x/θ ), find k such that
interval from 0 to kx is a (1 − α)100% confidence interval for the parameter
θ.
(4) Show that the (1 − α)100% confidence interval


σ
σ
X − zα/2 · √ , X + zα/2 · √
n
n
is shorter than the (1 − α)100% confidence interval


σ
σ
X − z2α/3 · √ , X + zα/3 · √ .
n
n
(5) X1 , X2 are independent and uniformly distributed on [0, θ], 0 < α ≤ 12 . Find k such that interval from 0 to kx is a (1 − α)100% confidence interval for the parameter θ. 1