A little help with simple stats ...

Posted by Hong A Ng on Jan 30, 2014; 3:41pm
URL: http://spssx-discussion.165.s1.nabble.com/A-little-help-with-simple-stats-tp5724237.html

Hi everyone,

I am going through some practice questions from a study guide and have the answers; however I can't seem to figure out why the answer is that way. My mind just isn't wrapping around it. Would someone be able to provide me with some pointers?

q#1 

Your company focuses on individuals with a minimum of $100K in investments (about one million), though it offers more comprehensive services to those with over $500K and over $1 million. It is especially interested in data on those segments. It knows that individuals with $500K to $1 million in investments represent 20% of its market, while those with over $1 million in investments represent only 5%. Your marketing team wants information that is as accurate as possible. You have budget enough to complete 600 surveys. Would a disproportionate sample be the right choice for this survey? Why or why not? Would a disproportionate sample affect the overall reliability of the data on the population? What would the confidence interval at the 95% confidence level be for the population if 200 interviews were conducted with:
 

•   individuals with > $100K to < $500K in investments;
  
•   individuals with $500K to $1million in investments; and
  
•   individuals with > $1million in investments. 
  

Below is the answer; however I do not know where they came up with the 266 (I am assuming it's due to the disproportionate sample):

•   Since this is the equivalent of a sample size of 266, the confidence interval at the 95%
  confidence level would be +/-6 for the population 
  

q#2

0. 0. 
      What is the confidence interval at the 95% confidence level for Region 1 with a sample of 260 and for all Regions if the sample is 600? 
      

   Below is the answer, however I am not sure where they got the formulation (SQRT(2500 etc). Could someone exlapin?

   
   

   •   The confidence interval for Region 1 for a sample of 260 is approximately +/-6.1%
     SQRT(2500/260)*1.96
     
   •   The confidence interval for all regions based on a sample of 600 is
     approximately +/-4% (SQRT(2500/600)*1.96) 
     

Thank you so much friends!

0.