According to a study conducted by an organization, the proportion of Americans w

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 121 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 increased.

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 increasedincreased aboveabove 0.10 because the value of np(1minusp) is less than 10.

B) This is not necessarily evidence that the proportion of Americans who are afraid to fly has increasedincreased aboveabove 0.10 because the sample size n is more than 5% of the population.

C) This is not necessarily evidence that the proportion of Americans who are afraid to fly has increasedincreased aboveabove 0.10 because the probability of obtaining a value equal to or more extreme than the sample proportion is ____ , which is not unusual. (Round to four decimal places as needed.)

D. This is not necessarily evidence that the proportion of Americans who are afraid to fly has increasedincreased aboveabove 0.10 because the sample proportion, _______, is very close to 0.10. (Type an integer or a decimal.)

Explanation / Answer

we are given that
Po = 0.10

n1 = 1100 ,

phat = 121/1100

so we calculate the difference in proportion test as

z = (0.11-0.10)/(sqrt(0.1*0.9/1100))
= 1.105

now from the z table we check the p value as
0.86542

Hence C

C) This is not necessarily evidence that the proportion of Americans who are afraid to fly has increased above 0.10 because the probability of obtaining a value equal to or more extreme than the sample proportion is 0.8654 , which is not unusual. (Round to four decimal places as needed.)

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