Question

1. Let X ∼ Bin(124, p) with observed x = 78. Then, the 95% confidence interval for p is . To make the length of the 95% confidence interval for p not greater than 0.05, we need the sample size n to be at least . Based on the data, if we want to test H0 : p ≤ 0.6 against Ha : p > 0.6, we conclude at significance level α = 0.05.

2. Let F ∼ F4,7. Assume c1 satisfies P(F > c1) = 0.01 and P(F < c2) = 0.01. Then, c1 = and c2 = ,and P(F <−2.0)= .

The Answers should be: 1) [0.544, 0.714] or [0.541, 0.709]; 1537; H0. 2. 7.85; 0.0668; 0

F4,7. Assume c1 satisfies P(F > c1) = 0.01 and P(F < c2) = 0.01. Then, and P(F < -2.0) = (3 points). Let F ~ and c2 = C1 (3 points). Let X ~ Bin(124, p) with observed x = 78. Then, the 95% confidence interval for To make the length of the 95% confidence interval for p not greater p is Based on the data, if we want than 0.05, we need the sample size n to be at least to test Ho : p< 0.6 against Ha : p > 0.6, we conclude at significance level a = 0.05.

Answer 1

Solution Sample proportion, ß = 2 = 78 124 = 0.629 Standard error of proportion, st = JA (1-P)/n = 10. 629* (1 ~ 0.629)/124 =0.04338 z-value for asy. Cil is 1.96 Eorror, E = *SE =1096*0.04338 - 0.085 ass. ст л е д, (0.629-0.085, 0-629 +0.085) (o.544 0.714) fog naagin of gros, E = 0.05/2 = 0.025 Sample size, n= (zlE) **P(1-P) = (1-9610.02s)? *0.629*(-0.629) - 1435 Since, p=0.6 lies in 95%. Confidence interval four pe we fail to reject to and conclude that there is no significant evidence that P >0.6 al significance level of a=0.05