Question

1- Most real estate offers are conditional on the buyer obtaining the necessary financing to complete the purchase. Based on past​ experience, one of​Canada's largest real estate agencies believes that​ 4% of the sales fail because the buyer is unable to obtain the financing approval from their mortgage broker or lender. The real estate agency has recently submitted 60 different​ offers, all of which are conditional on financing.

What is the sampling distribution model of the proportion of clients in this group who may not receive the necessary funding to purchase the​ house? Round to one decimal.

A. Mean​ = 4.0%; standard deviation​ = 0.3%

B. Mean​ = 4.0%; standard deviation​ = 2.5%

C. Mean​ = 96.0%; standard deviation​ = 2.5%

D. Mean​ = 96.0%; standard deviation​ = 0.3%

2- The director of admission of a large university is interested in determining the proportion of students who would like to live on campus in the coming academic year. Rather than examine the records for all​ students, the director randomly selects 150 students and finds that 108 of them would like to live on campus. Using a​ 90% confidence​ interval, what is the estimated true proportion of students who would like to live on campus in the coming academic​ year?

A.0.72​ ± 0.04457

B.0.72​ ± 0.060301

C.0.72​ ± 0.089582

D.0.72​ ± 0.028135

Answer 1

#Given:

p=0.04

n=60

#Mean=p=0.04=4%

#standard deviation=sqrt(p*(1-p)/n)=sqrt(0.04*(1-0.04)/60)=0.0253=2.5%

B. Mean​ = 4.0%; standard deviation​ = 2.5%

Option B is correct

Ansb:

Given that,

n = 150

x = 108

Point estimate = sample proportion = = x / n = 108 / 150=0.72

1 -    = 1- 0.72 =0.28

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z  0.05 = 1.645 ( Using z table )

Margin of error = E Z/2 *(( * (1 - )) / n)

= 1.645 *((0.72*0.28) / 150)

E = 0.060301

A 90% confidence interval is ,

E

0.72 0.060301

B.0.72​ ± 0.060301

Option c is correct