A nationwide study in 2003 indicated that 95% of college students with cell phon

Question

A nationwide study in 2003 indicated that 95% of college students with cell phones send and receive text messages with their phones. Suppose a simple random sample of n=1136 of college students with cell phones is obtained.

(a). Let Phat denote the sample proportion of college students with cell phones who send and receive text messages. Find the following.

(i). E(Phat)

(ii). SD(Phat)

(b). What is the sampling distribution model for Phat?(Check with the rule of thumb np?10 and n(1-p)?10.)

(C).What is the probability that 1065 or fewer college students in the sample send and receive text messages with their cell phones?

(d).If you want to reduce SD(Phat) by half, how much larger does the sample size n needs to be?

Explanation / Answer

i) E(Phat) = np=1136 x 0.95=1079.2

ii)SD(Phat)= sqrt(npq)=sqrt(1136 x 0.95 x (1-0.95)) =7.3457

iii) Sampling distribution model= Normal distribution

iv)Probability that 1065 or fewer college students in the sample send and receive text messages with their cell phones =P(x<1065) =P(z(=1065-1079.2)/7.3457)<-1.93)

from Normal distribution area table P(z<-1.93)= 0.5-0.4732=0.0268

v) if SD(Phat) is reduced to half i.e 7.3457/2=3.6785

sqrt(npq)=sqrt(n x 0.95 x (1-0.95)) =3.6785

   nx0.95x0.05 =3.67852

n=285

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