According to a survey in a country, 31% of adults do not have any credit cards.
ID: 2933349 • Letter: A
Question
According to a survey in a country, 31% of adults do not have any credit cards. Suppose a simple random sample of 700 adults is obtained.
(a) Describe the sampling distribution of p, the sample proportion of adults who do not have a credit card. Choose the phrase that best describes the shape of the sampling distribution of p below.
A) Not normal because n0.05N and np(1p)10.
B) Approximately normal because n0.05N and np(1p)<10.
C)Approximately normal because n0.05N and np(1p)10.
D) Not normal because n0.05N and np(1p)<10.
Determine the mean of the sampling distribution of p
u^p=
Determine the standard deviation of the sampling distribution of p
sigma^p=
b)In a random sample of 700 adults, what is the probability that less than 30% have no credit cards?
The probability is = ?
c)Would it be unusual if a random sample of 700 adults results in 252 or more having no credit cards?
A. The result is unusual because the probability that p is greater than or equal to this sample proportion is less than 5%.
B. The result is not unusual because the probability that p is greater than or equal to this sample proportion is less than 5%.
C. The result is unusual because the probability that p is greater than or equal to this sample proportion is greater than 5%.
D. The result is not unusual because the probability that p is greater than or equal to this sample proportion is greater than 5%.
Explanation / Answer
a)
C)Approximately normal because n0.05N and np(1p)10.
he mean of the sampling distribution of p =0.31
standard deviation of the sampling distribution of p =(p(1-p)/n)1/2 =(0.31*(1-0.31)/700)1/2 =0.0175
b)
probability that less than 30% have no credit cards =P(X<0.30)=P(Z<(0.30-0.31)/0.0175)
=P(Z<-0.5721)=0.2836
c)here sample proportion =phat =252/700=0.36
hence probability of 252 or more having no credit cards =P(X>0.36)=P(Z>(0.36-0.31)/0.0175)
=P(Z>2.8603)=0.0021
A. The result is unusual because the probability that p is greater than or equal to this sample proportion is less than 5%.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.