аЯрЁБс;ўџ ўџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ§џџџ* . !#"$&%(',)+ўџџџ-ўџџџўџџџ/0123456789:;<=ўџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџRџџџџџџџџ РFњ~э*žП@#CompObjџџџџџџџџџџџџ\WordDocumentџџџџ.џџџџы8ObjectPool ЭMь*žПњ~э*žПўџџџўџџџўџџџ ўџџџўџџџўџџџўџџџўџџџўџџџ !"#$%&'()ўџџџ+ўџџџўџџџўџџџўџџџ0ўџџџ23456789:;<=>?@ўџџџBўџџџўџџџEўџџџўџџџHўџџџJKLMNOPQRSTUVўџџџXўџџџўџџџ[ўџџџўџџџ^ўџџџ`abcdefghijkўџџџmўџџџўџџџўџџџўџџџrўџџџtuvwxyz{|}~ўџџџўџџџџџ РFMicrosoft Word 6.0 DocumentўџџџNB6WWord.Document.6;џў аЯрЁБс;џў LЫ,шшаЯрЁБс;џў  ЁdЗxpr  Œ  "  ОЁР currentpoint  П" О,Times .џ+ z, Symbol +aЁРЪ/MTsave save def 40 dict begin currentpoin_1006695441џџџџџџџџРFЭMь*žП€cць*žПOle џџџџџџџџџџџџPIC џџџџLPICT џџџџџџџџџџџџt 3 -1 roll sub neg 3 1 roll sub 416 div 480 3 -1 roll exch div scale currentpoint translate 64 59 translate /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (z) 0 261 sh /f2 {ff matrix dup 2 .22 put makefont dup /cf exch def sf} def 224 /Symbol f2 (a) 139 357 sh end MTsave restore  ПЁd$MATH7 ƒz „a џаЯрЁБс;џў ўџџџџџРFMicrosoft Equation Editor 2.0ўџџџDNQE Equation.2аЯрЁБс;џў аЯрЁБс;џў  ƒz „aаЯрЁБсCompObj џџџџYObjInfoџџџџ џџџџEquation Native џџџџџџџџџџџџ4_1006695511 РF€cць*žП€cць*žПмЅhSР eцы8Ь2ј2јј2ј2ј2ј2ј2’3’3’3’3’3Ђ3В3@’3Ж7[ђ3pb4"„4„4„4ˆ4ˆ4ˆ4Ž7777777&8Xi8‚Ж7ј2ˆ4  „4ˆ4ˆ4ˆ4Ж7ˆ4ј2ј2„4ђ3ˆ4ˆ4ˆ4ˆ4ј2„4ј2„4Ž7 32>3Tј2ј2ј2ј2ˆ4Ž7ˆ4ˆ4 Sample Final Exam for Stat. 224. Prof. Callan 1. a) Suppose A,B,C are independent events with probabilities P(A) = .6, P(B) = .4, P(C) = .3. Find (i) P(A(B) (ii) P(A(B) (iii) P(A|B) (iv) P(exactly one of A,B,C occurs) b) True(T) or False(F)? [Circle one] (i) The sample standard deviation of a set of data points is always larger than its standard deviation. T F (ii) The value of  EMBED Equation.2  is greater than the value of  EMBED Equation.2  with n degrees of freedom for all significance levels ( and all positive integers n. T F (iii) For every distribution, the sample mean of a random sample is an unbiased estimator of the population mean. T F (iv) For every normal distribution, the sample variance of a random sample is an unbiased estimator of the population variance. T F (v) Looking on a criminal trial as a hypothesis test, the American legal system is set up to consider a Type II error as more serious than a Type I error. T F 2. a) In a casino game, two dice are rolled simultaneously. You win $12 if the two dice show different numbers. What is a fair price to play this game? _______ b) If there are 11 cars in a race, in how many different ways can they place first, second, and third? _______ c) A high school class committee is composed of 4 women and 2 men. If the class consists of 20 men and 20 women, in how many ways can the committee be formed? ______ Is this number larger than or less than a million? [Circle one] 3. A blood test for a certain rare disease comes up positive in 98% of people who have the disease, but also has a 1% false positive rate. Suppose that 1 in 10,000 persons has the disease. a) If your test comes up positive, what is the probability you actually have the disease? _______ b) If your test comes up negative, what is the probability you have the disease anyway? _______ 4. a) A sample of 45 import cars yielded an average selling price of $18,500 with a sample standard deviation of $1,700. Based on this data, find a 95% confidence interval for the true mean selling price of import cars. ________________________ b) A sample of 200 urban voters yielded 145 in favor of Proposition X, and a sample of 360 rural voters yielded 200 in favor. Find a 95% confidence interval for the difference between the proportions of urban and rural voters in favor of the Proposition. ___________________________ 5. a) For a polling organization to assert with 95% confidence that its estimated proportion is correct within (4 percentage points, how large a sample will be needed? ______ b) Let ( denote the average gas mileage (miles per gallon) of a certain line of cars. Suppose the null hypothesis that ( = 30 is to be tested against the alternative that ( < 30 using a sample of 20 cars. Suppose also that it is known the standard deviation of the gas mileage is ( = 2.7. If the significance level is to be 5%, use Table 8 to estimate the Type II error probability when ( = 28. 6. One hundred observations of a random variable X yielded the following results X 0 1 2 3 4 frequency 29 35 26 11 5 Test at the 5% level if these results are consistent with a binomial distribution of n = 4 trials. Hint. First use the formula ( = np for the mean of a binomial distribution to estimate p from the data. 7. In a linear regression problem with n = 80 pairs  EMBED Equation.2 , the following quantities were calculated.  EMBED Equation.2   EMBED Equation.2   EMBED Equation.2  26.4 20.5 22.1 Find a 98% confidence interval for the slope of the regression line. ______________________ 8 a) A sample of 81 from a normal population yielded a sample standard deviation of s = .318. Find a 95% confidence interval for the population standard deviation. _______________________ b) In a one-way analysis of variance problem, a different treatment was applied to k = 5 samples each of size n = 13. The following sums of squares were computed: SST = 79.9 SS(Tr) = 13.2 Test at the 5% level the hypothesis that the treatments are equally effective. PAGE  PAGE 1 Ё–™ Ї8Ј„|PHHк(џсџтљFP(ќPHHк(d'd"rў\*аЯрЁБс;џў џџџўџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџOle џџџџџџџџџџџџPIC  џџџџLPICT џџџџџџџџџџџџ‘CompObjџџџџ*YаЯрЁБс;џў L„м,шшаЯрЁБс;џў ‘ ЁdЗxpr  Œ  "  ОЁР currentpoint  П" О,Times .џ+ t, Symbol +aЁРЫ/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 352 div 480 3 -1 roll exch div scale currentpoint translate 64 59 translate /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (t) -14 261 sh /f2 {ff matrix dup 2 .22 put makefont dup /cf exch def sf} def 224 /Symbol f2 (a) 84 357 sh end MTsave restore  ПЁd$MATH1 ƒt „a џаЯрЁБс;џў ўџџџџџРFMicrosoft Equation Editor 2.0ўџџџDNQE Equation.2аЯрЁБс;џў аЯрЁБс;џў  ƒt „aаЯрЁБсаЯрЁБс;џў LŒ”,шшObjInfoџџџџџџџџ,Equation Native џџџџџџџџџџџџ-4_1006699206џџџџџџџџРF€cць*žП€cць*žПOle џџџџџџџџџџџџ.PIC џџџџ/LPICT џџџџџџџџџџџџ1тCompObjџџџџAYObjInfoџџџџџџџџCаЯрЁБс;џў т!ЁdЗxpr  Œ !"! ОЁР currentpoint  П" О,Times .џ+ ()x +i ( ,)y +i ( )ЁРч/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1056 div 480 3 -1 roll exch div scale currentpoint translate 64 59 translate /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } 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length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (S) -3 261 sh 224 ns (xy) 186 357 sh end MTsave restore  ПЁd'MATHD ƒS ƒxƒy џўџџџўџџџўџџџ…†‡ˆ‰Š‹ŒўџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџўџџџџџРFMicrosoft Equation Editor 2.0ўџџџDNQE Equation.2аЯрЁБс;џў аЯрЁБс;џў  ƒS ƒxƒyаЯрЁБсўџ ђŸ…рOљhЋ‘+'Гй0н˜з @` f r ~Š’ šІУ 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