ࡱ> ^`[\] ɂbjbj S-LL<l$$KKKKK#######$&`)#N^#KKT$&&&KK#&#&&:}",#Kq" #j$0$"R)v)#)#&##&$)L U: CHI-SQUARE GENETICS PRACTICE PROBLEMS 1. A poker-dealing machine is supposed to deal cards at random, as if from an infinite deck. In a test, you counted 1600 cards, and observed the following: Spades 404 Hearts 420 Diamonds 400 Clubs 376 Fill in the table and run the Chi-square test. Card FaceObservedExpectedO-E(O-E)2(O-E)2/ESpadesHeartsDiamondsClubs Chi Square Sum = Degrees of Freedom: ___________ Accept of Reject Null Hypothesis: ________________________________________________________ 2. A genetics engineer was attempting to cross a tiger and a cheetah.She predicted a phenotypic outcome of the traits she was observing to be in the following ratio 4 stripes only: 3, spots only: 9, both stripes and spots.When the cross was performed and she counted the individuals she found 50 with stripes only, 41 with spots only and 85 with both.Run the Chi-Square Test (Hint: Calculate the percents of observed and expected) RatiosObserved #Expected #O-E(O-E)2(O-E)2/EStripes OnlySpots OnlyStripes/Spots Chi Square Sum =Degrees of Freedom: ___________ Accept of Reject Null Hypothesis: ________________________________________________________ 3. In the garden pea, yellow color (Y) is dominant to green (y), and round pod shape (R) is dominant to the constricted form (r). Considering both of these traits jointly in self-fertilized dihybrids (dihybrid cross), theprogeny appeared in the following numbers (9:3:3:1 ratio): 556 yellow, round 193 green, round 184 yellow, constricted 61 green, constricted Do these genes assort independently? Support your answer using Chi-square analysis. RatiosObserved #Expected #O-E(O-E)2(O-E)2/Eyellow, roundgreen, round yellow, constrictedgreen, constricted Chi Square Sum =Degrees of Freedom: ___________ Accept of Reject Null Hypothesis: ________________________________________________________ Hardy-weinberg practice problems 1) If 9% of an African population is born with a severe form of sickle-cell anemia (ss), what percentage of the population will be more resistant to malaria because they are heterozygous(Ss) for the sickle-cell gene? 2) 1 in 1700 US Caucasian newborns have cystic fibrosis. C for normal is dominant over c for cystic fibrosis. a) What percent of the above population have cystic fibrosis (cc or q2)? b) Calculate the allelic frequencies of p and q for this example. c) Now, calculate the genotypic frequencies for the population. 3) 4 in 2000 US Caucasian newborns have Tay Sachs Disease. T for normal is dominant over t for Tay Sachs Disease. a) What percent of the above population have Tay Sachs Disease (tt or q2)? b) Calculate the allelic frequencies of p and q for this example. c) Now, calculate the genotypic frequencies for the population. ANSWERS 1. expectedexpectedobserved(percent)(counts)z4040.254000.2004200.254001.0004000.254000.0003760.25400-1.200chi-square->2.480critical value->7.815 Compute each z from its own row as (observed-expected)/sqrt(expected). Be sure to use the counts in this formula, not the percentages. The chi-square statistic is the sum of the squares of the z-values. The number of degrees of freedom is 3 (number of categories minus 1). The critical value is from a table youll have on the exam (using ( = 0.05). 3. A genetics engineer was attempting to cross a tiger and a cheetah. She predicted a phenotypic outcome of the traits she was observing to be in the following ratio 4 stripes only: 3 spots only: 9 both stripes and spots. When the cross was performed and she counted the individuals she found 50 with stripes only, 41 with spots only and 85 with both. According to the Chi-square test, did she get the predicted outcome? Chi-square = S (O-E)2/E D.F. Value 1 3.841 2 5.991 3 7.815 Set up a table to keep track of the calculations: Expected ratioObserved #Expected #O-E(O-E)2(O-E)2/E4 stripes50446360.823 spots41338641.949 stripes/spots8599-141961.9816 total176 total176 total0 totalSum = 4.74 4/16 * 176 = expected # of stripes = 44 3/16 * 176 = expected # of spots = 33 9/16 * 176 = expected # stripes/spots = 99 Degrees of Freedom = 3 - 1 = 2 (3 different characteristics - stripes, spots, or both) Since 4.74 is less than 5.991, I can accept the null hypothesis put forward by the engineer. 4.) 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In this dihybrid cross: Observed55618419361Expected55918618662 The total observed is 994, so I found the expected values as so: 9/16= x/994 x= 559 3/16= x/994 x= 186 1/16= x/994 x= 62 Chi square= [(556-559)2 /559] + [ (184-186)2/186] + [ (193-186)2/ 186] + [(61-62)2/62] = (0.016) + ( 0.02) + ( 0.26) + (0.016) = 0.312 df= 3 p value from table at 0.05 is 7.815 My calculated value is much lower than the p value from the table, so we cannot reject the null hypothesis. 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