Question

A researcher visited 60 nests in an area with limited food resources available to the egret. He noted that each female would only produce four eggs in each nest. His observations are tabulated as below: No. of female chicks in each nesto 1 2 34 Observed frequency(no. of nests)11172363 Test whether or not the sexes of the offspring reflect a binomial distribution with p = q = 0.5 where p is the probability to have a female chick. Question 42 Not yet answered Marked out of 1.00 Flag question What is the expected probability for having 3 males offspring in the nest? Select one: O a. 0.375 ob. 0.5 C. 0.25 O d. 0.0625 Question 43 Not yet answered Marked out of 1.00 Flag question What is the calculated chi-square statistic and the degree of freedom? Select one: o a. X=19.84, d.f. =5 O b. X=20.16, d.f. =4 O c. XP=20.16, d.f. =5 o d. X=19.84, d.f. =4 Question 44 Not yet answered Marked out of 1.00 Flag question What conclusion can be drawn from the result? Select one: o a. Critical X > Calculated X, accept Ho, the sexes of offspring follow a binomial distribution with p = q = 0.5 (p>0.05) O b. Critical X <Calculated X , reject Ho, the sexes of offspring do not follow a binomial distribution with p = q=0.5 (p<0.001) c. Critical X < Calculated X, accept Ho, the sexes of offspring follow a binomial distribution with p = q = 0.5 (0.001<p<0.05) o d Critical X < Calculated x', reject Ho, the sexes of offspring do not follow a binomial distribution with p = 0 = 0.5 (0.001<p<0.05) Question 45 Not yet answered Marked out of 1.00 Flag question Test whether or not the sexes of the offspring reflect a binomial distribution with p=0.3 and q=0.7 where p is the probability to have a female chick. What conclusion can be drawn from the result? Select one: O a. Critical Calculated X , reject Ho, the sexes of offspring follow a binomial distribution with p=0.3 and q = 0.7 (0.001<p<0.005) Critical X> Calculated X, accept Ho, the sexes of offspring do not follow a binomial distribution with p = 0.3 and q = 0.7 (p>0.1) C. O Critical X > Calculated X', accept Ho, the sexes of offspring do not follow a binomial distribution with p = 0.3 and q = 0.7 (p<0.001) O d. Critical Calculated x reject Ho, the sexes of offspring do not follow a binomial distribution with p = 0.3 and q = 0.7 (p<0.001)

Answer 1

* Solution :- The problem is to test Hoi Binomial disth is good fit to the given data with p=9= 05 Hi : Binomial disth is not good fit with p=9=0.5 VS For testing this, first we estimate the parameters - n f fx x 0 11ooli-X = {fx. ΣΕ I 17 17 2 23 46 3 6 la 4 3 12 X = 1.55 For Binomial dist mean = E(X)= np . Using method of momests, we take ° = np p= X 93 P-loss a. p = 0.3875 = 3= 1-² = 0.6125

for -lable & filling P(x)= of duth & arranon expected frequencies. Ei= NP(2) 0.1407 0.3562 0.3379 0.1426 0.0225 0.999 ) 8.442 21.372 20. 274 8.556 1.35 59.99 60 & Table for test statistic- Oi Ei 02/E; IL 8.442 14.3330 17 21.392 13.5223 23 20.274 26.0925 as 6 8.5560 8.1768 13 1.35 39.906 62.1246 Here Op = Observed frequencies - E; - Expected frequencies As last two frequencies are less than 5 they are combined. a Test statistic - X = 032_N. DELE; 62.1246-60 = 2.1246 2 Table value - At sl. lo.s. - In-k-1,4 = 14-1-1 = A2 = 5.99) Here n= No. of independent groups = 4 K = No, of parameters estimated = 1

Decision - As Xcal < xz, we accept Ho at 57.d.o.s. Conclusion - Binomial dists is good fit to the given data with p=q=0.5 * Answers Q. 42] The expected prob. for having 3 males off springs in the nest - Prob. that next is having I female = 0.3562 offspring 9. 43 x cal = 2.12 & df. = 2 9.44] As Xcal < Xtabs accept Ho that offspring - follows binomial disth with p=9=0.5 8.45) - For p=0.3, q=0.7 offsprings do not follow binomial disth with p=q=0.5.