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Unformatted text preview: MGT 2250 — Lesson 29 _,
Determining Sample Size
For Specified Type I & Type II errors
' April 13, 2011 If alpha and beta are speciﬁed, the sample size “n” can be determined to
ensure that neither of them will be exceeded. Note: The zscores for
alphas and betas of the same value are the same. For example: zalpha
for alpha = 0.05 is 1.645, and the z—beta for beta = 0.05 is also 1.645.
Note also that alpha and beta can also be eXpressed as the percent
probability of making a Type I or type II error respectively. We'will now work through some examples. _ 1 a) A quality control (QC) manager must decide whether to accept a shipment of
batteries from a supplier or return it due to unacceptable quality. The quality requirements for these batteries demand that they have a useful life of at least 120'
hours. To test the quality of the shipment, a sample of batteries will be selected at random and tested. If the sample indicates a mean useful life of this shipment is
significantly less than 120 hours, the shipment will be rejected. (Note: The
population standard deviation (sigma) is known to be 12 hours.) What size “n” will be required to hold the probability of making a type I error to 5% and also a Type
II error to 5% if the actual life of this population of batteries is 115 hours? I742 pee/ﬂ MW) YZ/L) Z LZQSampleSizeTlééTZanrs 1 b) What size “n” will be required to hold the probability of making a Type I
error to 5% and also a Type 11 error to 5% if the actual life of this population of batteries is 112 hours?
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7t 0/11. W i “L
(/Q/OV/[L/ [ﬂ I a
1 c) What size “n” will be required to hold the probability of making a Type
error to 5% and also a Type II error to 5% if the actual life of this population of batteries is 118 hours? ‘, 1 d) What size “n” will be required to hold the probability of making a Type I L 7 @
error to 5% and a Type II error to 10% if the actual life of this population of 3 batteries is 115 hours? 1 e) What Size “n” will be required to hold the probability of making a Type 1 " error to 1% and a Type II error to 5% if the actual life of this population of batteries is 115 hours? (/QOr//T)Z 1 1) What size “n” will be required to hold the probability of making a Type
error to 1% and a Type II error to 1% if the actual life of this population of batteries is 115 hours? 8 g f a?! 3 Q‘s—x “WWW—pg rah—mm, a» ,mmw L29SampleSizeTl&T2Errors ...
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 Summer '08
 Milne

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