2011 National Survey of Fishing, Hunting, and ... - Census Bureau

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generalized variance function are estimated using direct replicate variances. These generalized variance parameters provide a relatively easy method to obtain approximate standard errors for numerous characteristics. Table D-2 provide the generalized variance parameters for FHWAR data. Methods for using the parameters to calculate standard errors of various estimates are given in the next sections. Standard Standard Errors Errors of Estimated of Estimated Numbers. Numbers. The approximate The approximate standard standard error, sx error, , of an sx , estimated of an estimated number number shown shown in this in report this report can can Standard be Errors obtained be obtained of Estimated using the using following Numbers. the following formulas. The approximate formulas. Formula Formula standard (1) is used (1) error, is to used scalculate x , of to an calculate estimated the standard the number standard errors shown errors of levels in of this levels of sportspersons, report of sportspersons, can be obtained anglers, Standard anglers, using wildlife-watchers. Errors and the following wildlife-watchers. of Estimated formulas. Numbers. Formula The (1) approximate is used to calculate standard the error, standard errors of levels of sportspersons, anglers, and wildlife watchers. sx , of an estimated number shown in this report can be obtained using the following formulas. Formula (1) is used to calculate the standard errors of levels of sportspersons, anglers, and wildlife-watchers. s 2 s 2 ax ax (1) bx (1) (1) x bx x 2 Here, x Here, is the x Here, size is the of x the size is the estimate of size the of estimate and the a estimate and and b a are and the b a parameters are and the b are parameters the in parameters the tables in the associated in tables the tables associated with associated the with particular the with particular the characteristic. (1) particular characteristic. characteristic. Formula Formula (2) Here, is Formula used (2) x is for is the used (2) standard size is for used of standard the errors for estimate standard of errors aggregates, and errors of a aggregates, and of i.e., b aggregates, are trips, the i.e., days, parameters trips, i.e., and days, trips, expenditures. in and days, the expenditures. tables and expenditures. associated with the particular characteristic. Formula (2) is used for standard errors of 2 s 2 cx s aggregates, ax i.e., ax bx trips, 2 bx days, and expenditures. 2 x (2) x (2) y 2y (2) s 2 ax bx cx x (2) Here, x Here, is again x Here, is the again x size is the again of the size the estimate; of size the of estimate; y the is the estimate; base y is the of y the base is the estimate; of base the of estimate; and the a, estimate; yb, and and a, c and b, are and a, the b, c parameters are and the c are parameters the in parameters the tables in the associated with ated the with particular ated the with particular the characteristic. particular characteristic. characteristic. in tables the tables associ- associ- Here, x is again the size of the estimate; y is the base of the estimate; and a, b, and c are the parameters in the tables associated of Illustration the with Computation of the the particular of Computation the Computation of characteristic. the Standard of the of Standard the Error Standard of Error Estimated Error of an Estimated of an Number Estimated Number Illustration Illustration Number Suppose Table there Illustration 1 Table were in this 1 an in report estimated of this the report shows Computation 37,397,000 shows that 33,916,000 that persons of 33,916,000 the persons Standard age 16 persons 16 years Error years 16 old old years of and and older Estimated older and who either older either Number either fished fished fished or or hunted hunted or hunted in in the the in United United the United States States in in States in 2006. 2011. 2006. Using Using formula formula (1) (1) with (1) the the with parameters the parameters a a = -0.000027 –0.000070 a = -0.000027 and and b b = and = 6,125 16,823 b = 6,125 from from table from table D-7, table D-2, the D-7, the approximate the approximate standard standard error the of estimate Table the estimated 1 in number this report number of 33,916,000 shows of of 33,916,000 37,397,000 that sportspersons 33,916,000 sportspersons persons 16 years 16 age old years 16 and years old older and old is older and older is either is fished or hunted in the United States in standard error of error of 2006. Using formula (1) with the parameters a = -0.000027 and b = 6,125 from table D-7, the approximate standard error of 2 the estimate number of 33,916,000 sportspersons 16 years old 2 and older is s x s x 0 . 000027 0. 000027 33, 916 33, 000 , 916, 000 6, 125 6, 125 33, 916 33, 000 , 916, 000 420, 330 420, 330 The 95-percent The 95-percent The confidence 95-percent confidence interval confidence interval for the interval estimated for the for estimate the number estimate number of sportspersons number of 2 s sportspersons of sportspersons 16 years 16 old years 16 and old years older and old is older from and is older 35,968,000 from is 33,092,000 from to 33,092,000 to to 38,826,000, 34,740,000, i.e., 34,740,000, 37,397,000 ie., 33,916,000 ie., ± 33,916,000 x 0. 000027 33, 916, 000 6, 125 33, 916, 000 420, 330 1.96 ± x 728,857. 1.96 ± x 1.96 420,330. Therefore, x 420,330. Therefore, a conclusion Therefore, a conclusion that a conclusion the that average the that average estimate the average estimate derived estimate derived from all derived from possible all from possible all possible samples samples lies The within samples 95-percent lies a within range lies within confidence a computed range a range computed interval this computed way in for this would the in way estimate this be would way correct number would correct for be roughly of correct sportspersons for roughly 95 for percent roughly 9516 percent of years 95 all percent possible old of all and possible of samples. older all possible is samples. from samples. 33,092,000 to 34,740,000, ie., 33,916,000 ± 1.96 x 420,330. Therefore, a conclusion that the average estimate derived from all possible Suppose Table there samples 1 Table were shows 1 lies an shows that estimated within 12,510,000 that a range 12,510,000 13,674,000 hunters computed hunters 16 in years this 16 age old years way 16 and years would old older and old be engaged older and correct older engaged in for who 219,925,000 roughly in engaged 219,925,000 95 percent in days 281,884,000 of days of participation all of possible participation days of in samples. participation in formula 2011. formula Using (2) with formula (2) the with parameters (2) the with parameters the a = parameters -0.000235, a = -0.000235, a b = –0.000284, -85,241, b = -85,241, and b = c = –127,863, and 22,698 c = 22,698 from and c table from = 46,699 D-9, table the from D-9, approximate table the approximate D-2, the standard standard error on error on 2006. in 2006. Using Using approximate 219,925,000 Table standard 219,925,000 1 shows estimated error that estimated on 12,510,000 281,884,000 days on days an estimated on hunters estimated an estimated 16 base years days of base on old 12,510,000 and of estimated 12,510,000 older hunters engaged base hunters is of in 13,674,000 219,925,000 is hunters days of is participation in 2006. Using formula (2) with the parameters a = -0.000235, b = -85,241, and c = 22,698 from table D-9, the approximate standard error on 2 219,925,000 estimated days on an estimated base of 12,510,000 hunters is 2 2 22, 698 22 2 , 698 219 , 925 219, 000 , 925, 000 s x s x 0 . 000235 0. 000235 219, 925 219, 000 , 925, 000 85, 241 85, 241 219, 925 219, 000 , 925, 000 7, 592 7, 000 , 592, 000 12, 510 12, 000 , 510, 000 2 2 22, 698 219, 925, 000 s x 0. 000235 219, 925, 000 85, 241 219, 925, 000 7, 592, 000 12, 510, 000 The 95-percent The 95-percent confidence confidence interval interval on the on estimate the estimate of 219,925,000 of 219,925,000 days is days from is 205,044,000 from 205,044,000 to 234,806,000, to 234,806,000, ie., 219,925,000 ie., 219,925,000 ± 1.96 ± x 1.96 7,592,000. x 7,592,000. Again, Again, a conclusion a conclusion that the that average the average estimate estimate derived derived from all from possible all possible samples samples lies within lies within a range a range The 95-percent computed The computed confidence 95-percent in this in way this confidence interval would way would be interval the correct estimate be correct on for the roughly of for estimate 281,884,000 roughly 95 percent of 95 219,925,000 days percent of is all from possible of days all 253,295,000 possible is samples. from samples. 205,044,000 to 310,473,000, to 234,806,000, i.e., ie., 219,925,000 281,884,000 ± ± 1.96 1.96 x x 7,592,000. 14,586,000. Again, Again, a conclusion a that that the the average estimate derived from from all all possible samples lies lies within within a range a range Standard computed computed Standard Errors in this in Errors this of way Estimated way would of Estimated would be Percentages. correct be correct Percentages. for for roughly The roughly reliability The 95 reliability percent 95 percent of an of estimated of all of an possible all estimated possible percentage, samples. percentage, samples. computed computed using sample using sample data for data both for both numerator numerator and denominator, and denominator, depends depends on the on size the of size the of percentage the percentage and its and base. its base. Estimated Estimated percentages percentages are relatively are relatively more more Standard reliable Errors Standard reliable than of Estimated the Errors than corresponding the of Percentages. corresponding Estimated estimates Percentages. The estimates reliability of the The of numerators the of reliability an numerators estimated of of the an of percentages, percentage, estimated the percentages, percentage, computed particularly particularly using computed if the sample percentages if the using data percentages sample for are both 50 data are percent 50 for percent both numerator more. and numerator denominator, more. When and When the denominator, numerator depends the numerator on and depends the the and size denominator the of on the denominator percentage size of of the the of percentage and the its percentage base. are and Estimated in its are different base. in different percentages Estimated categories, categories, percentages are use relatively the use parameter the are more parameter relatively in the more in the reliable tables than reliable the tables indicated corresponding than indicated by the the corresponding by numerator. estimates the numerator. of estimates the numerators of the numerators of the percentages, of the percentages, particularly particularly if the percentages if the percentages are 50 percent are 50 percent or more. When or more. the numerator When the and numerator the denominator and the denominator of the percentage of the are percentage in different are categories, in different use categories, the parameter use the in parameter the in the tables indicated The tables approximate The by indicated approximate the numerator. standard by the standard error, numerator. serror, x,p, can s x,p, be can obtained be obtained by use by of use the of formula the formula The approximate The approximate standard error, standard s x,p , can error, be obtained s x,p, can be by obtained use of the by formula use of the formula s x, p s ax bx s ,p x s ,p bp( 100 bp( 100 p) p) ,p , bp x ( 100x p) x p Here, x Here, is the x total is the number total number of sportspersons, of sportspersons, x, phunters, hunters, etc., which etc., which is the base is the of base the of percentage; the percentage; p is the p percentage is the percentage (3) x (3) (0 ≤ p (0 ≤ ≤ p ≤ 100); and 100); b is and the b parameter is the parameter in the in tables the tables associated associated with the with characteristic the characteristic in the in numerator the numerator of the of percentage. the percentage. Here, x is the Here, total x number is the total of sportspersons, number of sportspersons, hunters, etc., hunters, which etc., is the which base of is the percentage; base of the percentage; p is the percentage; p is the percentage and b is the (0 ≤ p ≤ parameter Illustration in 100); the Illustration tables and of b the associated is the of Computation the parameter Computation with the in of the characteristic the tables of Standard the associated Standard in Error the numerator with Error of an the Estimated of characteristic of an the Estimated percentage. Percentage in the Percentage numerator of the percentage. Table Illustration 1 Table shows 1 shows that of of the that the Computation of 12,510,000 the 12,510,000 hunters of the hunters Standard 16 years 16 old years Error and old of older, and Estimated older, 18.3 percent 18.3 Percentage percent hunted hunted migratory migratory birds. birds. From table From D-7, table D-7, the appropriate the appropriate b parameter b parameter is 5,756. is 5,756. Using Using formula formula (3), the (3), approximate the approximate standard standard error on error the on estimate the estimate of 18.3 of percent 18.3 percent is is 68 2011 National Survey of Fishing, Hunting, and Wildlife-Associated Recreation—Vermont U.S. Fish and Wildlife Service and U.S. Census Bureau Table 1 shows that of the 12,510,000 hunters 16 years old and older, 18.3 percent hunted migratory birds. From table D-7, the appropriate b parameter is 5,756. Using formula (3), the approximate standard error on the estimate of 18.3 percent is cx (3) (3)
Illustration of the Computation of the Standard Error of an Estimated Percentage Suppose there were an estimated 13,674,000 hunters age 16 years old and older of whom 18.9 percent hunted migratory birds. From table D-2, the appropriate b parameter is 15,798. Using formula (3), the approximate standard error on the estimate of 18.9 percent is 5, 756 18. 3 100 , . 18. 3 , 5 5756 , 756 1818 3. 3 100 100 1818 . 3 . 3083 . s xp s , xp , 12, 510, 000 083 . 083 . 12 12 , 510 , 510 , 000 , 000 s xp Consequently, the 95-percent confidence interval for the estimate percentage of migratory bird hunters 16 years old and older Consequently, is from Consequently, 16.7 the percent 95-percent the the to 19.9 95-percent confidence percent, confidence interval ie. 18.3 for interval ± interval 1.96 the estimate x for 0.83. for the the percentage estimate estimate percentage of migratory of of bird migratory hunters bird bird 16 hunters hunters years 16 old 16 years and years older old and and older olde is from 16.3 is is from percent from 16.7 16.7 to percent 21.5 percent percent, to to 19.9 19.9 i.e., percent, percent, 18.9 ie. ± ie. 1.96 18.3 18.3 x ± 1.33. 1.96 ± 1.96 x 0.83. x 0.83. Standard Error of a Difference. The standard error of the difference between two sample estimates is approximately equal to Standard Error Standard of a Error Difference. Error of of a a Difference. The standard The The error standard standard of the error error difference of of the the between difference two between between sample two two estimates sample sample is estimates approximately is is approximately equal to equal equal to to 2 2 sxsy s x y x2s2 sxy 2 2 (4) s s (4) (4) x y xysy (4) where where s x and where sx and s y are sx and sy are the standard errors of the estimates x and y. The estimates can be numbers, percentages, ratios, etc. This will represent where the sy standard are the standard errors of errors the estimates of the x and y. The x and estimates y. The can be numbers, can percentages, ratios, etc. ratios, This etc. This sx and the actual sy are the standard standard error errors quite of accurately the estimates for the x and difference y. The estimates between estimates can be numbers, of the same percentages, characteristic ratios, in etc. two This will represent different will will the areas, represent actual or the for standard the actual the actual difference standard error standard quite between error accurately error quite quite separate for accurately the and difference uncorrelated for for the the between difference characteristics estimates between between in of estimates the the same same of of area. the characteristic the same However, same characteristic in if two there in in two two different a high different areas, different positive or areas, for areas, (negative) the or difference or for for the correlation the between difference between separate between between the and separate two separate uncorrelated characteristics, and and uncorrelated characteristics the formula characteristics in will the overestimate same in in the area. the same same However, (underestimate) area. area. if However, there is the if true if there there is is a high standard positive a high a high error. (negative) positive positive correlation (negative) correlation between between the between two characteristics, the the two two characteristics, the formula the the will formula formula overestimate will will overestimate (underestimate) (underestimate) the true the the true true standard standard error. standard error. error. Illustration of the Computation of the Standard Error of a Difference Illustration Illustration of the Computation of of the the Computation of the Standard of of the the Error Standard of Error a Error Difference of of a a Difference In Table 8, of the 11,655,000 females in the age range of 18-24, 726,000 or 6.2 percent are sportspersons. Similarly, of the Suppose 11,638,000 In there In Table Table were males 8, 8, an of of the estimated in the the 11,655,000 same 13,608,000 age females range, females females 1,929,000 in in the the age in age the range or range age 16.6 of range percent of 18-24, 18-24, of 18-24 are 726,000 726,000 sportspersons. of whom or 6.2 6.2 percent 726,000 percent The are apparent or are 5.3 sportspersons. percent difference were between Similarly, of of the the sportspersons. the percent 11,638,000 Similarly, of female males males suppose in and in the male the same there same participants age were age range, range, estimated is 10.4 1,929,000 percent. 12,909,000 or or 16.6 16.6 Using percent males percent formula in are are the (3) sportspersons. same and age the appropriate range The The of apparent whom apparent b parameter 2,160,000 difference from or between between table 16.7 percent D-7, the the percent were approximate percent sportspersons. of of female female standard and The male errors male apparent participants of 6.2 difference percent is is 10.4 10.4 and between percent. 16.6 percent. the percent Using percentage Using are formula formula 0.55 of and female (3) (3) 0.85, and and and the respectively. the male appropriate sportspersons Using b b parameter formula is 11.4 from (4), from table the table percent. approximate Using D-7, D-7, the formula the standard approximate (3) and error standard the standard of appropriate the estimated errors errors of b of parameter 6.2 difference 6.2 percent percent from of and and 10.4 table 16.6 16.6 percent percent D-2, percent the is are approximate are 0.55 0.55 and and 0.85, standard 0.85, respectively. errors of Using 5.3 Using percent formula formula (4), (4), the the and 16.7 percent approximate are 0.79 standard standard 1.35, error error respectively. of of the the estimated Using difference formula of (4), of 10.4 the 10.4 percent approximate percent is is standard error of the estimated difference of 11.4 percent is 2 2 s x s y 055 . 20 2 x s xy y 055 . 2. 85 102 055 0 . 85 2. . 0. 85 102 . 102 . The 95-percent confidence interval on the difference between 18-24 year old female and male sportspersons is from 8.4 to The 95-percent 12.4, The The i.e., 10.4 95-percent confidence ± 1.96 confidence interval x 1.02. Since interval interval the the difference on interval on the the between difference does not 18- between contain between to 24-year-old zero, 18-24 18-24 we year year can female old conclude old female and female male with and and male sportspersons 95 male percent sportspersons confidence is from is is from 8.3 that from 8.4 the 8.4 to to to 14.5, percentage i.e., 12.4, 12.4, 11.4 i.e., i.e., of ± 10.4 1.96 18-24 10.4 ± x 1.96 ± year 1.56. 1.96 x old Since 1.02. x 1.02. female the Since Since interval the interval does not does contain not contain zero, we zero, can we conclude can with 95 with percent 95 percent confidence that the that the percentage of 18- to of 24-year-old 18-24 year female old 15.8 sportspersons the interval female sportspersons to 17.6, i.e., is 16.7 is less does less is than ± than not less 1.96 the contain the than x percentage 0.45. percentage zero, we of can 18-24 conclude year old with male 95 sportspersons. percent confidence that the percentage of 18-24 year old female sportspersons is less than the the percentage of 18- of to of 18-24 24-year-old 18-24 old male old male male sportspersons. Standard Errors of Estimated Averages. Certain mean values for sportspersons, anglers, etc., shown in the report were calculated Errors Standard as Standard the of ratio Errors Estimated Errors of two of of numbers. Averages. Estimated For Certain Averages. example, mean Certain Certain average values mean mean for days values sportspersons, values per for angler for sportspersons, is anglers, calculated etc., anglers, as: anglers, shown etc., etc., in shown the shown report in in the were the report report calculated as the lated lated ratio as as of the the two ratio ratio numbers. of of two two For numbers. example, For For average example, days average average per angler days days per is per calculated angler angler is is as: calculated as: were were calcu- calcu as: x y total days x x total days total days total anglers y y total total anglers Standard errors for these averages may be approximated by the use of formula (5) below. Standard Standard errors Standard for errors these errors for averages for these these averages may averages be approximated may may be be approximated by the use by of by the formula the use use of of (5) formula formula below. (5) (5) below. below. x s 2 s x s s s r ss x y x y x y (5) (5) y x 2 s s s y 2 r ss x y x y x y (5) y x 2 s r ss x y x y x y y (5) y x y 2 xy2 xy xy In formula In formula (5), r (5), represents r represents the correlation the correlation coefficient coefficient between between the numerator the numerator and the and denominator the denominator of the of estimate. the estimate. In the In the above formula, In formula use 0.7 (5), as r an estimate the of r. 15.8 to 17.6, i.e., 16.7 between ± 1.96 the x 0.45. above In formula, use (5), 0.7 r represents as an estimate the correlation of r. coefficient between the numerator and and the the denominator of of the the estimate. In In the the above above formula, formula, use use 0.7 0.7 as as an an estimate estimate of of r. r. Illustration Illustration of the of Computation the Computation of the of Standard the Standard Error Error of an of Estimated an Estimated Average Average Illustration of of the the Computation of of the the Standard Error Error of of an an Estimated Average Average Suppose Table that 2 the shows estimated that the number average of days the per average angler days 16 per years angler old and age older 16 years for all old fishing and older was for 17.3 all days. fishing Using was 16.7 formulas days. (1) and Using (2) formulas Table above, Table 2 (1) we shows 2 shows and compute that (2) that above, the the the average standard average we compute days error days per on the per angler total standard angler days, 16 16 years error years 516,781,000, old on old total and and older days, and older for total 553,841,000, for all anglers, all fishing fishing 29,952,000, was and was 17.3 total 17.3 days. anglers, days. to be Using 15,828,079 Using 33,112,000, formulas formulas and to (1) (1) and and be 20,329,124 399,342, (2) (2) above, above, and respectively. 693,033, we we compute compute respectively. The the approximate the standard standard The error approximate standard error on on total error total days, standard on days, the 516,781,000, estimated error on the average and estimated and total total of anglers, 17.3 anglers, average days 29,952,000, is of 16.7 days to to isbe 15,828,079 and and 399,342, 399,342, respectively. The The approximate standard standard error error on on the the estimated average average of of 17.3 17.3 days days is is 2 2 2 2 516, 781, 000 158, 280, 079 2 2 516 781 000 s xy 2 , , 158 , 280, 079 399, 342 15, 828, 079 399, 342 s xy 2 07 . 0 40 29, 952, 000 516 . , 781, 000 s xy 516, 781, 000 158 280, 079 29 399, 342 15, 828, 079 399, 342 399, 342 15, 828, 079 399, 342 2 07 . 0. 40 29, 952, 000 516, 781, 000 29, 952, 000 , 952, 000 2516 07 . , 781, 000 29, 952, 000 0. 40 29 952, 000 516, 781, 000 29 952, 000 516 516 , 781 , 781 , 000 , 000 2929 , 952 952 , 000 , 000 Therefore, the 95-percent confidence interval on the estimated average of 16.7 days is from 15.8 to Therefore, 17.6, i.e., the 16.7 95-percent ± 1.96 x 0.45. confidence interval on the estimated average of 17.3 days is from 16.5 to Therefore, 18.0, i.e., the the 17.3 95-percent ± 1.96 x 0.40. confidence interval interval on on the the estimated average average of of 17.3 17.3 days days is is from from 16.5 16.5 to to 18.0, 18.0, i.e., i.e., 17.3 17.3 ± 1.96 ± 1.96 x 0.40. x 0.40. U.S. Fish and Wildlife Service and U.S. Census Bureau 2011 National Survey of Fishing, Hunting, and Wildlife-Associated Recreation—Vermont 69 15.8 to 17.6, i.e., 16.7 ± 1.96 x 0.45.
Page 1:
U.S. Fish & Wildlife Service 2011 N
Page 4 and 5:
Economics and Statistics Administra
Page 6 and 7:
List of Tables Fishing and Hunting
Page 8 and 9:
Foreword When I was growing up, it
Page 11 and 12:
Highlights
Page 13 and 14:
Hunters Hunters are sportspersons w
Page 15 and 16:
Wildlife-Related Recreation Partici
Page 17 and 18:
Anglers Participants and Days of Fi
Page 19 and 20:
Hunters Participants and Days of Hu
Page 21 and 22:
Wildlife Watchers Participants and
Page 23 and 24:
2001-2011 Comparison Comparing the
Page 25 and 26:
Tables
Page 27 and 28: Table 1. Fishing and Hunting in Ver
Page 29 and 30: Table 6. Freshwater Anglers, Trips,
Page 31 and 32: Table 10. Saltwater Anglers, Trips,
Page 33 and 34: Table 14. Hunters and Days of Hunti
Page 35 and 36: Table 16. Summary of Expenditures i
Page 37 and 38: Table 18. Summary of Hunting Trip a
Page 39 and 40: Table 20. Expenditures in Vermont b
Page 41 and 42: Table 22. Summary of Vermont Reside
Page 43 and 44: Table 24. Wildlife Watching in Verm
Page 45 and 46: Table 28. Vermont Residents Partici
Page 47 and 48: Table 31. Expenditures in Vermont b
Page 49 and 50: Table 33. Wildlife-Watching Expendi
Page 51: Table 36. Participation of Vermont
Page 54 and 55: Appendix A. Definitions Annual hous
Page 56 and 57: State governments (such as State pa
Page 58 and 59: Appendix B. 2010 Participation of 6
Page 60 and 61: Table B-2. Selected Characteristics
Page 63 and 64: Appendix C U.S. Fish and Wildlife S
Page 65 and 66: was moved from a separate category
Page 67 and 68: Table C-1a. Comparison of Wildlife-
Page 69 and 70: Table C-1e. Comparison of Wildlife-
Page 71: Table C-3. Wildlife-Watching Partic
Page 74 and 75: Appendix D. Sample Design and Stati
Page 76 and 77: A. Screening Sample Every interview
Page 80: Table D-1. Approximate Standard Err
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