Answer to Question #124517 in Statistics and Probability for jse

Question

1. Dairy cows at large commercial farms often receive injections of bST (Bovine Somatotropin), a hormone used to spur milk production. Bauman et al. (Journal of Dairy Science, 1989) reported that 12 cows given bST produced an average of 28.0 kg/d of milk. Assume that the standard deviation of milk production is 2.25 kg/d.

(a) Find a 99% confidence interval for the true mean milk production.

Round your answers to two decimal places (e.g. 98.76).


_________ < = mu < = ______

(b) If the farms want the confidence interval to be no wider than ±1.25 kg/d, what level of confidence would they need to use?

Express your answer in percent.
Round your answer to the nearest integer (e.g. 98).

confidence = ____%

Answer 1

a) C I = x ± z_{α *}∂/√n C I = 28± 2.58*2.25/√12

C I = 28 ± 1.68, C I = ( 26.32 , 29.68)

b) z_α= m.E * √n/∂ , z_α=1.25*√12/2.25 , =1.92 we look for the probability of 1.92 from z tables which is 0.0274*2 =0.0548 = (1-0.0548)% = 94.52% = 95%