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Unformatted text preview: 121 STA 2023 c B.Presnell & D.Wackerly  Lecture 10 STA 2023 c B.Presnell & D.Wackerly  Lecture 10 122 Binomial Experiment p. 179 1. change in the basement. ¡ Thought: People who live in glass houses should identical trials in experiment. 2. Each trial results in one of two possible outcomes, ¢ or £ . ¥
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and 126 ¥ (ii) at most 2 contain errors. STA 2023 c B.Presnell & D.Wackerly  Lecture 10 STA 2023 c B.Presnell & D.Wackerly  Lecture 10 128 Ex. Select sample of items from a shipment, and count Ex. #4.51, p. 192 Supplier claims no more than 2 82 ¥
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y2 ¢ ¥ ¡ switches are defective. Sample of TREAT AS BINOMIAL A What is the expected number of defective switches? you expect? . If . What is the variance? $ ¥ If I toss a balanced coin 10 times, how many heads do A as a binomial random variable. Here $ students). Can treat $ Ex. Sample of 20 students at UF (more than 37,000 # who think statistics is an interesting subject switches, ? d
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2 xw8 ¥ ¢ yd D 8 NOT BINOMIAL If it is: $ is discrete defectives. Is ¥ ¤¡ ¥
¥ ¤¡ ¥ ¤ is discrete found ¥
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¥ 3 defective bin and , sometimes ¤¡ 700 good
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10 items ¤ is binomial with parameters If # defective in sample. . 129 score indicates that
is a “rare event”. 130 A Portion of Table II (p. 771) D – Reject the claim– STA 2023 c B.Presnell & D.Wackerly  Lecture 10 if the claim
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8 A – zscore for 4 is
is correct? D Is it likely that you would observe STA 2023 c B.Presnell & D.Wackerly  Lecture 10 n=10
p
k 0.01 ... 0.60 0.70 ... 0.99 0 .904 ... .000 .000 ... .000 The table of the binomial distribution (pp. 770–773) 1 .996 ... .002 .000 ... .000 gives cumulative binomial probabilities, i.e., it gives 2 1.000 ... .012 .002 ... .000 3 1.000 ... .055 .011 ... .000 4 1.000 ... .166 .047 ... .000 5 1.000 ... .367 .150 ... .000 6 1.000 ... .618 .350 ... .000 7 1.000 ... .833 .617 ... .000 8 1.000 ... .954 .851 ... .004 9 1.000 ... .994 .972 ... .096 . Any needed prob. can
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[from Table II, p. 913] ©
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w !¤ Ex. Conduct a survey, randomly select 10 indiv.: _
X<6 4 5 6 7 8 9 10 Interested in the number who are Lutherans
( X=7 ¥ w ¥ §
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¥ [from Table II] Lutheran, any other (or no) rel. afﬁl.) Interested in the number who are gun owners and
favor gun control.
( ¥¢ 3 gun owner who favors gun control, everyone else) ¥£ 2 ¥£ 1 A 0 ¥¢ ¥ (b) _
X<8 2 _
X<7 132 “more than 4 and no more than 8.” ¥
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 Spring '08
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 Statistics, Binomial

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