Re: A little help with simple stats ...

Posted by David Marso on Jan 30, 2014; 4:09pm
URL: http://spssx-discussion.165.s1.nabble.com/A-little-help-with-simple-stats-tp5724237p5724238.html

Hong,
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The Management
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Hong A Ng wrote

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
               
       
       
               
                       
                               
                                       
                                               
                                                       
                       
                               
                                       
                                               
                                                       
               
       
       
               
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!