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Unformatted text preview: MGT 2250 — Lesson 28
» Determining the Probability of Type II Errors
April 11, 2011 Deﬁnition: Type II errors are made when the mill hypothesis is NOT
rejected when it should have been (i.e. that the null hypothesis is
actually false and therefore the alternative hypothesis is true). The
symbo for the probability of making a Type 11 error is the Greek letter
beta ). _ While the beta is dependent on the alpha (and the “n” and the true
population mean), it is NOT equal to one minus the alpha! The
procedure for determining beta follows with an example. Example: 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 Sig batteries will be selected at
random and tested. If the sample indicates a mean useful life of this
shipment is signiﬁcantly less tha ours, the shipment will be
rejected. (Note: The population standard deviation (sigma) is known to
be ghours.) 1.) Develop and state the Nuli Hypothesis and the Alternative ch‘fth'tt.,‘ s
YPO esns or 18 es Hgo ‘ [L2 [91] H’dﬁ [‘7 410/0 2.) Based on the hypotheses, determine the type of hypothesis test: Onetail Upper (lTU), Onetail Lower (lTL) or
Two Tail (2T) ' [KT2L, 3.) Specify (set) the level of Signiﬁcance (alpha —VR) and
determine the rejection point  z,p. d2.0‘< Etfuo‘r‘ﬂéﬁ/{p L28TypeZErrors (H4, Hm “4 U 4.) Determining the beta if the true population mean is 115 hours.
WW ‘* M f «if
(/1 &\
/A6Tﬁ39§{)cz ,_ r, Pﬂ/ﬂﬂ A Pow%a;7;ﬂr%ﬁ/M A} WPKJJ I ﬂaw/Z: ’ 7? 5.) Determining the beta if the true population mean is 112 hours. 2'2 gf/(a/7/FHZZ [£2 //—/,ﬂr/96?/? ,50’7/
ﬂvﬂj/_,Doax 7,770? L2 8Type2Errors ‘ I _ 3 _ 6.) Determining the beta if the true population mean is 118 hours. a [IL/H 7.) Determining the “power” of the test. The porer curve. L28TypeZErrors 8.) Example #2: A marketing research ﬁrm basis its charges to clients on the
assumption that the average phone call lasts 15 minutes. A sample of
35 calls was done to test the assumption that the null hypothesis of the
mean being less than or equal to 15 minutes was true. In other words,
were the calls actually averaging more than 15 minutes in length?
The sample had a standard deviation of 4 minutes. At alpha=0.05,
what is the probability of making a Type 11 error if the mean is
actually 17 minutes? What is the power of the test? H’s ’{ « a v Cd; '\ [if ,5 a .x I “' ,m f are w”
9 /’ J t v. L28Type2Errors ...
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 Summer '08
 Milne

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