Question

According to a study conducted by an​ organization, the proportion of Americans who were afraid to fly in 2006 was 0.10. A random sample of 1,100 Americans results in 99 indicating that they are afraid to fly. Explain why this is not necessarily evidence that the proportion of Americans who are afraid to fly has decreased.

Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A. This is not necessarily evidence that the proportion of Americans who are afraid to fly has decreased below 0.10 because the value of ​np(1-​p) is less than 10.

B. This is not necessarily evidence that the proportion of Americans who are afraid to fly has decreased below 0.10 because the sample proportion, __________ is very close to 0.10

C. This is not necessarily evidence that the proportion of Americans who are afraid to fly has decreased below 0.10 because the sample size n is more than​ 5% of the population.

D. This is not necessarily evidence that the proportion of Americans who are afraid to fly has decreased below 0.10 because the probability of obtaining a value equal to or more extreme than the sample proportion is ______ which is not unusual.

Answer 1

for normal distribution z score =(p̂-p)/σp
here population proportion=     p=	0.100
sample size       =n=	1100
std error of proportion=σp=√(p*(1-p)/n)=	0.009

probability =

P(X<0.09)

=

P(Z<-1.11)=

0.1335

option D is correct

D. This is not necessarily evidence that the proportion of Americans who are afraid to fly has decreased below 0.10 because the probability of obtaining a value equal to or more extreme than the sample proportion is __0.1335____ which is not unusual.

( please try 0.1345 if this comes incorrect)