Check My Work eBook ExerciseZ A market research firm conducts telephone surveys
ID: 3067116 • Letter: C
Question
Check My Work eBook ExerciseZ A market research firm conducts telephone surveys with a 45% historical response rate. a. What is the probability that in a new sample of 400 telephone numbers, at least 125 indnnduals will cooperate and respond to the questions? In other words, what is the probabilitythet the samule pespetion nit e least 125/400 -0.31257 Calculate the standard error to 4 decimals Calculate the probability to 4 decimals, showing your steps along the way. b. If a follow-up study was completed a year later with only 64 telephone numbers, what is the prebatity that the response rate was betwemus nd 46%, Calculate the standard error to 4 decimals Caloulate the probablity to 4 decimals, showing your steps akong the way. s p sExplanation / Answer
Solution:- Given that p = 0.45 , q = 1-0.45 = 0.55 ,
a. n = 400
the standard error = sqrt(p*q/n) = sqrt(0.45*0.55/400) = 0.0249
=> p(p-bar >= 0.3125 ) = P(z >= (0.3125 - 0.45)/0.0249)
= P(z >= -5.5220)
= 1
b. For n = 64
P(0.44 <= p <= 0.46) = P((0.44 - 0.45)/sqrt(0.45*0.55/64) <= p <= (0.46 - 0.45)/sqrt(0.45*0.55/64) )
= P(-0.1608 <= p <= 0.1608)
= 0.5636 - 0.4364
= 0.1272