A systems engineer is experimenting with a system that has traditionally produce

Question

A systems engineer is experimenting with a system that has traditionally produced an average quality index of 10. She is experimenting with a new method, and she will produce n outputs that will have a variance 10. The sample mean of these n observations is denoted . She will attempt to determine if the underlying population mean differs from 10 using the test statistic l 10. What is the smallest value of n such that . the type I error rate is less than 5% and . the type II error rate is less than 10% if the population mean of the new method is 8?

Explanation / Answer

Answer:

Part1

Sample size for single mean

For 95%, z=1.96

d=2

variance =10

Sample size = (z2*s2)/d2

= (1.962*10)/22

=9.604

The sample size required= 10

Part2

Sample size for single mean

For 95%, z=1.96

for =0.10, z =1.282

d=2

variance =10

Sample size = ((1.96+1.282)2*s2)/d2

= (3.2422*10)/22

=26.276

The sample size required= 27

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