Question

Use the table below to calculate the answers to the questions that follow it. Be sure to write how you are calculating your answer. You must include the numbers from the table when showing your work. The following table shows a sample of CSI students who are interested attending the “CSI has talent” show and whether they live on Staten Island. Results of a survey follow

SI resident	Interested- Yes	Interested- No	Total
SI resident-Yes	100	70	170
SI resident-No	120	70	190
Total:	220	140	360

A) What proportion of students are interested in attending the show?

B) What proportion of SI residents are interested in attending show? What proportion of non-SI residents are interested in attending the show? Which type of student is more likely to be interested in attending the show?

C) Assume that the proportion of all CSI students who are interested in attending the show is 0.6, what is the sampling distribution of the proportion of students who are interested in attending the show based on a sample size of 360 students?

D) How likely is it that would get a sample proportion less than what we obtained in part a?

Answer 1

a) proportion of students are interested in attending the show=220/360=0.611

b) proportion of SI residents are interested in attending show =100/170=0.588

proportion of non-SI residents are interested in attending the show =120/190=0.632

non-CSI  student is more likely to be interested in attending the show

c)

the sampling distribution of  proportion of students who are interested in attending the show based on a sample size of 360 students follows normal distribution with parameter

estimated proportion p=0.6 and

std error of proportion=σp=√(p*(1-p)/n)=

0.0258

d)

probability that 0.6111 proportion or less will be interested in attending the show

for normal distribution z score =(p̂-p)/σp
here population proportion=     p=	0.600
sample size       =n=	360
std error of proportion=σp=√(p*(1-p)/n)=	0.0258

probability =

P(X<0.6111)

=

P(Z<0.43)=

0.6664