Page 357 - Applied Statistics And Probability For Engineers

c09.qxd 5/15/02 8:02 PM Page 305 RK UL 9 RK UL 9:Desktop Folder:

9-3 TESTS ON THE MEAN OF A NORMAL DISTRIBUTION, VARIANCE UNKNOWN 305

approximately. Thus, the probability of rejecting H : 0.82 if the true mean exceeds this
0
by 0.02 is approximately 1
1
0.10 0.90, and we conclude that a sample size of
n 15 is adequate to provide the desired sensitivity.
Minitab will also perform power and sample size computations for the one-sample t-test.
Below are several calculations based on the golf club testing problem:

Power and Sample Size

1-Sample t Test
Testing mean null (versus null)
Calculating power for mean null difference
Alpha 0.05 Sigma 0.02456
Sample
Difference Size Power
0.02 15 0.9117
Power and Sample Size
1-Sample t Test
Testing mean null (versus null)
Calculating power for mean null difference
Alpha 0.05 Sigma 0.02456
Sample
Difference Size Power
0.01 15 0.4425
Power and Sample Size
1-Sample t Test
Testing mean null (versus null)
Calculating power for mean null difference
Alpha 0.05 Sigma 0.02456
Sample Target Actual
Difference Size Power Power
0.01 39 0.8000 0.8029

In the first portion of the computer output, Minitab reproduces the solution to Example 9-7, veri-
fying that a sample size of n 15 is adequate to give power of at least 0.8 if the mean coefficient
of restitution exceeds 0.82 by at least 0.02. In the middle section of the output, we asked Minitab
to compute the power if the difference in and 0.82 we wanted to detect was 0.01. Notice
0
that with n 15, the power drops considerably to 0.4425. The final portion of the output is the
sample size required to give a power of at least 0.8 if the difference between and of interest
0
is actually 0.01. A much larger n is required to detect this smaller difference.
9-3.4 Likelihood Ratio Approach to Development of Test Procedures
(CD Only)

EXERCISES FOR SECTION 9-3
9-30. An article in the ASCE Journal of Energy Engineer- building material. Five samples of the material were tested in
ing (1999, Vol. 125, pp. 59–75) describes a study of the ther- a structure, and the average interior temperature (°C) reported
mal inertia properties of autoclaved aerated concrete used as a was as follows: 23.01, 22.22, 22.04, 22.62, and 22.59.