Question

1) You work for a marketing firm that has a large client in the automobile industry. You have been asked to estimate the proportion of households in Chicago that have two or more vehicles. You have been assigned to gather a random sample that could be used to estimate this proportion to within a 0.02 margin of error at a 99% level of confidence.

a) With no prior research, what sample size should you gather in order to obtain a 0.02 margin of error?

b) Your firm has decided that your plan is too expensive, and they wish to reduce the sample size required. You conduct a small preliminary sample, and you obtain a sample proportion of ˆp=0.205p^=0.205 . Using this new information. what sample size should you gather in order to obtain a 0.02 margin of error?

2) The confidence interval was (35, 45)

What was the point estimate?

What was the margin of error?

Answer 1

Question .1

E = margin of error = 0.02

c- level = confidence level =99% = 0.99

Area = 0.995

Using this area find the Zc (critical value) excel command =NORMSINV(0.995) or use normal table.

Zc = 2.58    ( critical value for 99% confidence level)

Part a.

p = no prior = 0.5       ( when no prior is given so consider it is 50% )

n = 4160.25

n = 4160     ( if they asked to round next whole number then conisder 4161 )

Part b

p = 0.205

n = 2712

Que.2

Confidence interval = (35, 45 )

lower limit = 35

upper limit = 45

Point estimate = 40

Margin of error (E) :

E = 5

Margin of error is 5