Question

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 0.04 margin of error at a 95% level of confidence.

a) With no prior research, what sample size should you gather in order to obtain a 0.04 margin of error? Round your answer up to the nearest whole number.

n = _____ households

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 ˆ p = 0.18 . Using this new information. what sample size should you gather in order to obtain a 0.04 margin of error? Round your answer up to the nearest whole number.

n = ____ households

Answer 1

a)

With no prior research , let sample proportion ,   p̂ =    0.5  
sampling error ,    E =   0.04  
Confidence Level ,   CL=   95%  
          
alpha =   1-CL =   5%  
Z value =    Zα/2 =    1.9600   [excel formula =normsinv(α/2)]
          
Sample Size,n =    (Z / E)² * p̂ * (1-p̂)=   600.2279  
          
          
so,Sample Size required=       601  
n=601 households

b)

sample proportion ,   p̂ =    0.18  
sampling error ,    E =   0.04  
Confidence Level ,   CL=   95%  
          
alpha =   1-CL =   5%  
Z value =    Zα/2 =    1.9600   [excel formula =normsinv(α/2)]
          
Sample Size,n =    (Z / E)² * p̂ * (1-p̂)=   354.3746  
          
          
so,Sample Size required=       355  
n=355 households