Question

You are to determine the size for a simple random sample based upon the following considerations. You are assigned the task of determining the average age of owners of Lincoln automobiles. The estimate for the standard deviation is 12. You are willing to accept a maximum error of +- 2 years of age. Furthermore, the level of confidence associated with your statistic should be 95%. Based on these criteria, what is the size of the sample you need to use?

a.) 139

b.) 216

c.) 456

d.) 907

Your task has now changed. You are now assigned the job of determining the percentage of Lincoln owners who either once owned or currently (also) own a Cadillac. You have no idea what the percentage is, so you assume maximum variation within the population. Your estimate needs to be within 3% points of the population parameter (.3). This time your client is asking you to product a statistic that has a 98% level of confidence. In this case, how large should your simple random sample be?

a.) 426

b.) 632

c.) 965

d.) 1,496

Last year, you took a simple random sample designed to determine the average income of owners of Lincoln automobiles. The sample of 1,200 respondents was designed to be within $4,000 of the population parameter. This year, your client wants more exact data and has asked you to cut the allowable error in half to be within $2,000. Based on that change, how large does the new simple random sample need to be?

a.) 600

b.) 1,200

c.) 2,400

d.) 4,800

Answer 1

1)

for 95 % CI value of z=	1.960
standard deviation σ=	12.00
margin of error E =	2
required sample size n=(zσ/E)2                                         =	139.0

2)

here margin of error E =	0.0300
for98% CI crtiical Z          =	2.320
estimated proportion=p=	0.5000
required sample size n =	p*(1-p)*(z/E)2=	1496.00

3)

new simple random sample =1200*2² =4800