Applied Statistics and Probability for Engineers

approximately. Thus, the probability of rejecting H 0 :  0.82 if the true mean exceeds this

by 0.02 is approximately 1

 1 0.10  0.90, and we conclude that a sample size of

n15 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:

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

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 we wanted to detect was 0.01. Notice

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  0 of interest

is actually 0.01. A much larger nis required to detect this smaller difference.

9-3.4 Likelihood Ratio Approach to Development of Test Procedures

(CD Only)

EXERCISES FOR SECTION 9-3

 0 0.82

Power and Sample Size

1-Sample t Test

Testing meannull (versusnull)

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 (versusnull)

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 (versusnull)

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

9-30. An article in the ASCE Journal of Energy Engineer-

ing(1999, Vol. 125, pp. 59–75) describes a study of the ther-

mal inertia properties of autoclaved aerated concrete used as a

building material. Five samples of the material were tested in

a structure, and the average interior temperature (°C) reported

was as follows: 23.01, 22.22, 22.04, 22.62, and 22.59.

c 09 .qxd 5/15/02 8:02 PM Page 305 RK UL 9 RK UL 9:Desktop Folder: