ࡱ> AC @_  /bjbj >nbb '::|$I<@[I]I]I]I]I]I]I$KMIIIWWW[IW[IWW=@pq2!>"GII0I>pNpND@pN@`"WIIIpN: Z: AP Statistics Second Semester Exam Review Answers 1) Suppose we want a 90% confidence interval for the average amount spent on books by freshmen in their first year at a major university. The interval is to have a margin of error of $2, and the amount spent has a normal distribution with a standard deviation EMBED Equation.DSMT4. The number of observations required is EMBED Equation.DSMT4 EMBED Equation.DSMT4 n = 608.86 number of observations = 609 2) Scores on the SAT Mathematics test (SAT-M) are believed to be normally distributed. The scores of a random sample of three students who recently took the exam are 550, 620, and 480. A 95% confidence interval for EMBED Equation.DSMT4 based on these data is Confidence interval is: EMBED Equation.DSMT4 EMBED Equation.DSMT4 95% confidence interval is: EMBED Equation.DSMT4 or (376.11, 723.89) 3) The following represents some computer output that relates the number of Manatee deaths to the number of powerboats registered in Florida. Predictor Coef StDev t ratio P Constant -41.430 7.412 -5.59 .000 Boats 0.12486 0.01290 9.68 .000 Write the least squares regression line for predicting the number of manatee deaths from the number of powerboat registrations. EMBED Equation.DSMT4 What is the intercept of the least-squares regression line? The intercept is -41.430. In the context of the problem it would mean that if there were no boats registered, then we would have an increase of 41.430 manatees. It doesnt make sense in this problem. Interpret the slope of the line in the context of the problem. The slope of 0.12486 means that as the number of powerboats registered in Florida increases by 100, the number of manatee deaths increases by 12.5. 4) Birth weights at a local hospital have a normal distribution with a mean of 110 oz. and a standard deviation of 15 oz. Find the proportion of infants with birth weights between 125 oz. and 140 oz. Since there is a normal distribution of weights, we can use the z-calculations to find the answer. EMBED Equation.DSMT4 Look in the z-table for the proportion with a z-score less than 1.0 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 5) The heights (in inches) of males in the United States are believed to be normally distributed with mean EMBED Equation.DSMT4. The average height of a random sample of 25 American adult males is found to be 69.72 inches and the standard deviation of the 25 heights is found to be EMBED Equation.DSMT4. The standard error of the mean is standard error = EMBED Equation.DSMT4 6) Referring to the information in question 5, if the t-test statistic is found to be 1.75. At what level is this finding significant? Look up a z-score of 1.75 in the z-table. A z-score of 1.75 corresponds to a p-value of .0401. We can say that the finding would be significant at the 5% level of EMBED Equation.DSMT4. 7) Bags of a certain brand of tortilla chips claim to have a net weight of 14 ounces. Net weights actually vary slightly from bag to bag and are normally distributed with mean EMBED Equation.DSMT4 and standard deviation .2. In a random sample of 10 bags of tortilla chips, what is the probability that the mean net weight is between 13.7 and 14.3? Since we have a sample of size 10, we need to use the sample size as part of our calculation. EMBED Equation.DSMT4 Look in the z-table for the proportion with a z-score less than -.47 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 8) Dentists are increasingly concerned about the growing trend of local school districts to grant soft drink companies exclusive rights to install soda pop machines in schools in return for money that goes directly into school coffers. According to a recent study by the National Soft Drink Association, 62% of schools nationally already have such contracts. This comes at a time when dentists are seeing an alarming increase in horribly decayed teeth and eroded enamel in the mouths of teenagers and young adults. With ready access to soft drinks, children tend to drink them all day. That, combined with no opportunity to brush, leads to disaster, dentists say. Suppose that 20 schools around the county are randomly selected and asked if they have a soft drink contract. What is the probability that at most 8 of these schools have contracts? This is a binomial setting for probability. EMBED Equation.DSMT4 Enter it in the calculator as Binomcdf (20,.62,8). 9) In a process for manufacturing glassware, glass stems are sealed by heating them in a flame. The temperature of the flame varies a bit. Here is the distribution of the temperature X measured in degrees Celsius: Temperature540545550555560Probability0.10.250.30.250.1 Find the mean temperature EMBED Equation.DSMT4 and the standard deviationEMBED Equation.DSMT4. This is a probability distribution, so we can use the probability formulas for expected value: EMBED Equation.DSMT4 EMBED Equation.DSMT4 To find the standard deviation, take the square root of the variance: EMBED Equation.DSMT4 You can do the calculations in the calculator by putting the temperature data in L1 and the probabilities in L2. You can find the mean and standard deviation by doing 1-variable statistics L1,L2. (Stat >>>CALC>>>1-Var Stats L1, L2) 10) Consider a screening test for prostate cancer that its maker claims will detect the cancer in 85% of the men that actually have the disease. One hundred seventy-five men who have been previously diagnosed with prostate cancer are given the screening test, and 141 of the men are identified as having the disease. Does this finding provide evidence that the screening test detects the cancer at a rate different from the 85% claimed by its manufacturer? We need to do a hypothesis test to test the sample results against the claim. Follow the PHANTOMS procedure. P: Proportion of prostate cancer detected in men using a screening test. H: EMBED Equation.DSMT4 EMBED Equation.DSMT4 A: Assume SRS of men with prostate cancer. Our sample is less than 10% of the population. There are more than 1750 men in the US with prostate cancer. We have a possibility for more than 10 successes and 10 failures in the sample: EMBED Equation.DSMT4 N: 1-proportion z-test T: EMBED Equation.DSMT4 O: p-value = .10 EMBED Equation.DSMT4 M: Retain the null hypothesis. S: We do not have enough statistical evidence, p-value of .10 at EMBED Equation.DSMT4, to reject the null hypothesis. We must retain the null hypothesis that the screening test for prostate cancer successfully detects cancer is 85% of patients with prostate cancer. 11) A geneticist hypothesizes that half of the given population will have brown eyes and the remaining half will be evenly split between blue and green-eyed people. In a random sample of 60 people from this population, the individuals are distributed as shown in the table below. Perform a goodness of fit test of the geneticists hypotheses about eye color. Brown EyesGreen EyesBlue EyesObserved341511Expected301515 P: Population will have the proportion of eye color that a geneticist believes is correct. H: EMBED Equation.DSMT4 A: All expected counts are greater than 5. There was a random sample of people from the population. See table for expected counts. N: Chi-Square Goodness of Fit test T: EMBED Equation.DSMT4 df=2 O: p-value = .449 EMBED Equation.DSMT4 M: Retain the null hypothesis. S: We do not have enough statistical evidence, p-value of .449 at EMBED Equation.DSMT4, to reject the null hypothesis. We must retain the null hypothesis that the proportion of eye color for the population is the same as what the geneticist believes is correct. One half the population will have brown eyes, 25% will have blue eyes and 25% will have green eyes. 12) A researcher wished to compare the average amount of time spent in extracurricular activities by high school students in a suburban school district with that in a school district of a large city. The researcher obtained an SRS of 60 high school students in a large suburban school district and found the mean time spent in extracurricular activities per week to be EMBED Equation.BREE4hours with a standard deviation of EMBED Equation.BREE4hours. The researcher also obtained an independent SRS of 40 high school students in a large city school district and found the mean time spent in extracurricular activities per week to be EMBED Equation.BREE4with a standard deviation EMBED Equation.BREE4. Construct a 95% confidence interval for the difference in the mean time spent in extracurricular activities of the two groups. P: Difference in the mean time spent in extracurricular activities for students in a suburban school district and those students in a large city school district. A: SRS of both student groups Large sample size (60 and 40) so by the Central limit theorem we can assume normality of the sample distributions. N: 2-sample confidence interval I: EMBED Equation.DSMT4= EMBED Equation.DSMT4 df=98 EMBED Equation.DSMT4 C: We are 95% confident that the true difference in mean time spent in extracurricular activities between suburban district students and city students is 1.0078 to 2.9922. Since 0 is not within the interval, we are confident that there is a difference in the mean time spent by the 2 groups of students. 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`<Times New Romanww @w5 fm-2 (125140).1359`i``FTimes New Romanww @w5 fm- 2 Px`$Symbol Xww @w5 fm- 2 =_&1MathTypeUU%DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  P(125d"xd"140)==.1359E & -"System5 fm !-%TdDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  P(125d"xd"140)==.1359 FMathType 5.0 Equation MathType EFEquation.DSMT49q* pCompObjSV\iObjInfo^OlePres000UW_REquation Native i.  &N&@ & MathTypeP @Symbol ww 0wfe- 2 myp&MathTypeUUDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_AP %!AHA_D_E_E_A  m & "Systemfe !-$DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_AP %!AHA_D_E_E_A  m FMathType 5.0 Equation MathType EFEquation.DSMT49q_1368516307ZFo2!o2!Ole mCompObjY\niObjInfopW{ .  @&N & MathType` Times New Romanww 0w f- 2 4.15` Times New Romanww 0w f- 2 xy@Times New Romanww 0w fOlePres000[]qEquation Native _1368516306.`Fo2!o2!Ole - 2 sySymbolr ww 0w f- 2 =y&MathTypeUUDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_AP %!AHA_D_E_E_A  s x ==4.15 & "System f !-,DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_AP %!AHA_D_E_E_A  s x ==4.15 FMathType 5.0 Equation MathType EFEquation.DSMT49qCompObj_biObjInfoOlePres000acpEquation Native U* H $.    &N  & MathType-Ka59K9.--$ ^F)D0.0.CRC~AdQ--@L-K5,99-$ F7)00CC"AQ-- nTimes New Romanww @wfc- 2 4.15``Times New Romanww @wfc- 2 .83`Times New Romanww @wfc- 2 25nTimes New Romanww @wfc- 2 s5\Times New Romanww @wfc- 2 n5`SymbolR BXww @wfc- 2 ==X&EMathTypeUU9DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A   s n  == 4.15 25  ==.83 & --"Systemfc !-9\dDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A   s n  == 4.15 25  ==.83 FMathType 5.0 Equation MathType EFEquation.DSMT49q= {.  &N & MathType0 `_1368516305fFo2!o2!Ole CompObjehiObjInfoOlePres000gi6Equation Native _1368516304pdlFo2!p2!Ole Times New Romanww @wEf/- 2 .05B``Symbol -Tww @wEf/- 2 ay`Symbol eXww @wEf/- 2 =y{&MathTypeUUDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  a==.05 & "System/Ef/ !-TdDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  a==.05 FMathType 5.0 Equation MathTyCompObjkniObjInfoOlePres000mo,Equation Native pe EFEquation.DSMT49q4 x.  @&N & MathTypeP `Times New Roman w)w 0wNf- 2 14`@SymbolB  w)w 0wNf- 2 m4`Symbol2 i w)w 0wNf- 2 =4x&MathTypeUUDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_AP %!AHA_D_E_E_A  m==14 & "SystemNf !-M<DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_AP %!AHA_D_E_E_A  m==14 FMathType 5.0 Equation MathType EFEquation.DSMT49qr 9 _1368516303rFp2!p2!Ole CompObjqtiObjInfoOlePres000suEquation Native _1368516302jxFp2!p2!Ole .  @&N & MathType-e-'Bi,--$ ?"t%  3_E-- -!--z-' g  @ -$ " h  @ @  q ^  ---^ -m  n[Times New Romanww @whf-2 13.714``Times New Romanww @whf- 2 .47#`V Times New Romanww @whf- 2 2y Times New Romanww @whf- 2 10nTimes New Romanww @whf- 2 x0`LTimes New Romanww @whf- 2 z0=Times New Romanww @whf- 2 n0nSymbol Tww @whf- 2 m0V 2 s0nSymbol 'Tww @whf- 2 --`H 2 ===-,&MathTypeUUDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  z== x"-m s n  == 13.7"-14 2 10  =="-.47 & --"Systemhf !-TdDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  z== x"-m s n  == 13.7"-14 2 1      !"#$%&'()*+,-./0123456789:;<=>?ABCDEFILMNOPQRSTUVWXZ[\]`cdefghijklmnopqstuvwz}~0  =="-.47 FMathType 5.0 Equation MathType EFEquation.DSMT49q 4\ .  @ &N  & MathTypeP `<CompObjwziObjInfoOlePres000y{Equation Native .Times New Romanww @w1f-2 (.47).3192```FTimes 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!-‡TdDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  z== x"-m s n  == 14.3"-14 2 10  ==.47CompObjHiObjInfoJOlePres000KzEquation Native Y( FMathType 5.0 Equation MathType EFEquation.DSMT49qg 4R .  @ &N  & MathTypeP `<Times New Romanww @wf-2 (.47).6808```FTimes New Romanww @wf- 2 Pz`Symbol] Xww @wf- 2 =&MathTypeUU DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  P(zd".47)==.6808 & "Systemf !- TdDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  P(zd".47)==.6808 FMathType 5.0 Equation MathTy_1368516299Fp2!p2!Ole ^CompObj_iObjInfoape EFEquation.DSMT49q4 .  &N & MathTypeP-ss `<Times New Romanww @wf~-2 (13.714.3).3616``u```FOlePres000bEquation Native rK_1368516298vFp2!p2!Ole xTimes New Romanww @wf~- 2 Px`Symbol+ Xww @wf~- 2 =/_n&;MathTypeUU/DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  P(13.7d"xd"14.3)==.3616 & -"Systemf~ !-/\dDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  P(13.7d"xd"14.3)==.3616 FMathType 5.0 Equation MathType EFEquation.DSMT49q4LdDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  P(Xd"8)CompObjyiObjInfo{OlePres000Equation Native |P<3  %.  @ 6&N@6 & MathType  zV Symbol ww @wf- 2 (yz Symbol 7ww @wf- 2 )yz Symbol ww @wf- 2 (yz  Symbol 8ww @wf- 2 )yz Symbol ww @wf- 2 (yz Symbol 9ww @wf- 2 )yz$ Symbol ww @wf- 2 (yz Symbol :ww @wf- 2 )yz Symbol ww @wf- 2 (yz Symbol ;ww @wf- 2 )yzE Symbol ww @wf- 2 (yz! Symbol <ww @wf- 2 )yz) Symbol ww @wf- 2 (yzi, Symbol =ww @wf- 2 )yz- Symbol ww @wf- 2 (yz0 Symbol >ww @wf- 2 )yxV"Times New Romanww @wf-2 020119218812oooN o<Times New Romanww @wf-2 (8)(1)<`DTimes New Romanww @wf-2 20202020v 8 ^Times New Romanww @wf-72 .62.38.62.38.62.38....62.38.0381``X`x`@````G```STimes New Romanww @wf- 2 01283 d "Times New Romanww @wf- 2 knk|Times New Romanww @wf- 2 nyFTimes New Romanww @wf- 2 PXppTimes New Romanww @wf- 2 ky"Symbol CTww @wf- 2 -y*Symbol Tww @wf- 2 ^ 2 =-=* 2 "* 2 b.2 n n n n^V 2 ++++=  L, .2 n n n n.2 n n n n%&@MathTypeUU4DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  P(Xd"8)==nk()p k (1"-p) n"-k ==200().62() 0 .38() 20 ++201().62() 1 .38() 19 ++202().62() 2 .38() 18 ++...++208().62() 8 .38() 12 ==.0381 & "Systemf !-==nk()p k (1"-p) n"-k ==200().62() 0 .38() 20 ++201().62() 1 .38() 19 ++202().62() 2 .38() 18 ++...++208().62() 8 .38() 12 ==.0381 FMathType 5.0 Equation MathTy_1368516297F-p2!-p2!Ole CompObjiObjInfope EFEquation.DSMT49q{ Ox.  @&N & MathType` 2 Times New Romanww 0wgf- 2 xy@Symbol Xww 0wgf- 2 myx&MathOlePres000Equation Native _1368516296F-p2!-p2!Ole TypeUUDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_AP %!AHA_D_E_E_A  m x & "Systemgf !-4dDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_AP %!AHA_D_E_E_A  m x FMathType 5.0 Equation MathType EFEquation.DSMT49q{ Ox.  @&NCompObjiObjInfoOlePres000Equation Native  & MathType` 8 Times New Romanww 0w4fV- 2 xySymbol Xww 0w4fV- 2 syx&MathTypeUUDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_AP %!AHA_D_E_E_A  s x & "SystemV4fV !-4dDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_AP %!AHA_D_E_E_A  s x FMathType 5.0 Equation MathTy_1368516295F-p2!-p2!Ole CompObjiObjInfope EFEquation.DSMT49q42 Z.  0&N// & MathTypep  Symbol" Aww @wAfS- 2 (y  Symbol eww @wAfS- 2 )yo OlePres000ZEquation Native _1368516294F-p2!-p2!Ole  Symbol" Bww @wAfS- 2 (y  Symbol fww @wAfS- 2 )y Symbol" Cww @wAfS- 2 (y Symbol gww @wAfS- 2 )yY Symbol" Dww @wAfS- 2 (y Symbol hww @wAfS- 2 )y Symbol" Eww @wAfS- 2 (y~ Symbol iww @wAfS- 2 )y! 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Symbol kww @wAfS- 2 )y" Symbol" Hww @wAfS- 2 (y$ Symbol lww @wAfS- 2 )y[& Symbol" Iww @wAfS- 2 (yB) Symbol mww @wAfS- 2 )y) Symbol" Jww @wAfS- 2 (y+ Symbol nww @wAfS- 2 )yx Times New Romanww @wAfS-42 540.1545.25550.3555.25560.1550``*`$`*`1"Times New Romanww @wAfS- 2 xiiK@!Times New Romanww @wAfS- 2 xp(@Symbol pTww @wAfS- 2 mpSymbol" MTww @wAfS-2 ==++++=ASymbol qXww @wAfS- 2 pZ&MathTypeUUDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  m x ==@x i p i ==540().1()++545()  " .25()++550().3()++555().25()++560().1()==550 & "SystemSAfS !-ždDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  m x ==@x i p i ==540().1()++545()  " .25()++550().3()++555().25()++560().1()==550CompObjiObjInfoOlePres000Equation Native       !"#$%&()*+.123456789:;<=>?@ABCDEFHIJKLMNORUVWXYZ[\]^_`abcdefghijkmnopqrstux{|}~ FMathType 5.0 Equation MathType EFEquation.DSMT49q½\dDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  s x2 ==@x i "-m -EX .  >&N>= & MathType0 $ Symbol5 ɨww @wf- 2 (y  Symbole ww @wf- 2 )y. Symbol5 ww @wf- 2 (y Symbole ww @wf- 2 )y Symbol5 ww @wf- 2 (yZ  Symbole ww @wf- 2 )y#  Symbol5 ww @wf- 2 (y Symbole ww @wf- 2 )y Symbol5 ww @wf- 2 (yC Symbole ww @wf- 2 )y  Symbol5 ww @wf- 2 (yw Symbole ww @wf- 2 )y Symbol5 ww @wf- 2 (y8" Symbole ww @wf- 2 )y$ Symbol5 ww @wf- 2 (yf* Symbole ww @wf- 2 )y/ Symbol5 ww @wf- 2 (yC6 Symbole ww @wf- 2 )y7 Symbol5 ww @wf- 2 (y: Symbole ww @wf- 2 )y[ "Times New Romanww @wf- 2 2y2K"Times New Romanww @wf- 2 2y!"Times New Romanww @wf-2 22222 Times New Romanww @wf-C2 (540550.10545550.25550550.30555550(.25)56`0`*`0 ~`a1Times New Romanww @wf-2 0550.1032.5``A7"Times New Romanww @wf- 2 xixi>Times New Romanww @wf- 2 xp8Symbole Tww @wf- 2 sm9Symbol5 Tww @wf- 2 =-=h=2 -+-+-+-+-=6bSymbole Xww @wf- 2 m&MathTypeUUDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  s x2 ==@x i "-m x ()  "  2 p i ==540"-550() 2 .10()++545"-550() 2 .25()++550"-550() 2 .30()++555"-550() 2 (.25)++560"-550() 2 .10()==32.5 & "Systemf !-x ()  "  2 p i ==540"-550() 2 .10()++545"-550() 2 .25()++550"-550() 2 .30()++555"-550() 2 (.25)++560"-550() 2 .10()==32.5 FMathType 5.0 Equation MathType EFEquation.DSMT49q { _1368516293F-p2!-p2!Ole CompObjiObjInfoOlePres000Equation Native '_1368516292F-p2!-p2!Ole ,.  @@&N & MathType@-aCKjO-O--$ @\u?&FFY4Y`WFg- 2Times New Romanww @wVf-2 32.55.70`L`>Symbol Xww @wVf- 2 =y& MathTypeUUDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A   32.5  ==5.70 & --"SystemVf !-LdDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A   32.5  ==5.70 FMathType 5.0 Equation MathType EFEquation.DSMT49qCompObj-iObjInfo/OlePres0000Equation Native G*&{j .  @"&N`" & MathType` ITimes New Romanww @w{f-C2 (:.85 Proportion of prostate cancer dete ```~~ll`~`~ll`~`l;Times New Romanww @w{f-2 cted is .85l`l``u"Times New Romanww @w{f- 2 oyFTimes New Romanww @w{f- 2 HpASymbol mXww @w{f- 2 =p&MathTypeUUDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  H o :p==.85  Proportion of prostate cancer detected is .85 & "System{f !-|dDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  H o :p==.85  Proportion of prostate cancer detected is .85_1368516291F-p2!-p2!Ole PCompObjQiObjInfoS FMathType 5.0 Equation MathType EFEquation.DSMT49qM.{ .  @*&N) & MathType` OTimes New Romanww @w>f-COlePres000TEquation Native lB_1368516290F-p2!Tp2!Ole v2 (:.85 Proportion of prostate cancer dete```~~ll`~`~ll`~`lGTimes New Romanww @w>f-+2 cted is not equal to .85l`l`l`f`l``x"Times New Romanww @w>f- 2 ayFTimes New Romanww @w>f- 2 HpGSymbolu 3Xww @w>f- 2 p&2MathTypeUU&DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  H a :p`".85  Proportion of prostate cancer detected is not equal to .85 & "System>f !-&DdDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  H a :p`".85  Proportion of prostate cancer detected is not equal to .85 FMathType 5.0 Equation MathTyCompObjwiObjInfoyOlePres000zEquation Native pe EFEquation.DSMT49q^ .  @&N  & MathType ]Times New Romanww @w$fC-(2 10 175*.85148.75``````N``Times New Romanww @w$fC-%2 (1)10 175*.1526.25```N`:`]:Times New Romanww @w$fC- 2 np:Times New Romanww @w$fC- 2 npH]Symbol> Tww @w$fC- 2 =z > 2 -=&MathTypeUUDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  npe"10       175*.85==148.75n(1"-p)e"10   175*.15==26.25 & "SystemC$fC !-|dDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  npe"10       175*.85==148.75n(1"-p)e"10   175*.     JK !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHITM`NOPQRSUVW^XYZ[\]_cazbedhfgikjlmnpoqtrsuvwyx{|}~15==26.25 FMathType 5.0 Equation MathType EFEquation.DSMT49q&   .   &N & MathType -_1368516289FTp2!Tp2!Ole CompObjiObjInfoOlePres000N Equation Native _1368516288FTp2!Tp2!Ole 66-~99--$ g~00CC)--z-6 6:- ~  9n 9X-$  g f 0X0XCv C    --b v \STimes New Romanww @wMf- 2 yn Times New Romanww @wMf-2 .806.85```Times New Romanww @wMf- 2 1.64`Times New Romanww @wMf-2 (1).85*.15``` Times New Romanww @wMf- 2 175[n4Times New Romanww @wMf- 2 ppL`LTimes New Romanww @wMf- 2 zpTimes New Romanww @wMf- 2 ppNTimes New Romanww @wMf- 2 npn<SymbolO ^Tww @wMf- 2 ---`H 2 ===-, 2 --&MathTypeUUDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  z== p "-p  p(1"-p)n  == .806"-.85  .85*.15175  =="-1.64 & --"SystemMf !-ldDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  z== p "-p  p(1"-p)n  == .806"-.85  .85*.15175  =="-1.64 FMathType 5.0 Equation MathType EFEquation.DSMT49q= {CompObjiObjInfoOlePres0006Equation Native .  &N & MathType0 `Times New Romanww @w>f- 2 .05``SymbolE Tww @w>f- 2 ay`SymbolF Xww @w>f- 2 =y{&MathTypeUUDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  a==.05 & "System>f !-TdDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  a==.05_1368516287FTp2!Tp2!Ole CompObjiObjInfo FMathType 5.0 Equation MathType EFEquation.DSMT49q= {.  &N & MathType0 `Times New Romanww @w>f- OlePres0006Equation Native _1368516286FTp2!Tp2!Ole 2 .05``SymbolE Tww @w>f- 2 ay`SymbolF Xww @w>f- 2 =y{&MathTypeUUDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  a==.05 & "System>f !-TdDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  a==.05 FMathType 5.0 Equation MathType EFEquation.DSMT49qD~ۏ ^ڛ:sy䢑m/z_2Ed'G?;fƑ0 3μVs;*UvA8Q5h§n>:W[\KW~mTSU>!=3LIyDd J  C A@?"2 =ܦiNւ*Iy`!=ܦiNւ*I (dxTMhSAv7/i I[,P F ۔$SI#I%d Exx(z̓{OtW'x7=yW؏uЮX8d2>KM41 Ri^QrbNl[ZZ/_Wݛ's&}QѮAarvi>WRiP+^JU.ۙU&l*7EOo>M\x1;nePt|<4LzЂvFLP0K#朆Lzkl. o!I(zWў5ũVlc o$Kݏ&=6t3|ڝAt]&ڥ+5>^KQ^Zek}t]a,?XZDd J  C A@?"2MELK ZTTv2 'Z)y`!!ELK ZTTv2 'ZPg xuRAkQ۬m@6i{DSAiKh{M{I &EoUW$$1'C/ݓ!w{7gĮ(o6}3f73of4@֊HSz8FZVf5ȖЁOO%q{h c{%P:w{>H<-@e =T$=Zk̞\i6C|}UoNKbt[Z\.6ՍOJxnWJ0+fxo_\`& %AtUcI`*X)UPsWkvk7 ͛~ٻ27eIVoI3A!_\ˡ/R_HBqYɂ.a?lS>/{-N(L(pi8Ϭ5.yrб4qC:h¶؈?@fe m4_D=_;~G"MteZFݗ~dvx$$If!vh#vt":V l t065t"aytB3yDd  @J  C A@?"2/jB Yy`!/jB Y6" }xSMOSA=3mQF#BÖJpABKl X&-5ڕӸ?… &.GW+#hBb9H8ys}ws^NsY ǩj!K-]7v~cz@?haPS';tݲc,g*, zZeuSWpT$=#+Xvx* ~}/AxrYּVi^S_;ϷN\1Dhlzb":9QuԱYHvudsySpf6  EdWg̛ TU/Ai[jڕ& Dd P lJ   C A @?"22tB_ȺX 7 rwy`!tB_ȺX 7 rpxTOA~3PL=hPD!DJ8x(UWmn B Qz!$61b¶(MmcD,6RmAΞI~#G -4q:&2Ib&vZ,QibWg]Ϟkڃ8sYDgW9MKZ9Cp̮ Dz|;O"$;ǶzZ5SRar M[_+kkzrR^I&;U-%輨geSZ\7 7mH! )c!xR^_6Wrtyb85c Rd Vy, )硜VFF1ޟRj0;M[~W  9XCxDl ICRW[UsTb8c+]:/?9Z߸  ^XSOA]QajqY7PQ{` c(>sKݯeOpDd @J   C A @?" 2~ <"VzZGy`!R <"VzR ? 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