Two independent pollsters surveyed the same number of people from two different

Question

Two independent pollsters surveyed the same number of people from two different populations of approximately equal size. Pollster A concluded he was 95% confident the mean weight of his population is 150 + 16.3 lbs. Pollster B concluded she was 95% confident the mean of her population is 150 + 11.6 lbs. Which of the following statements are true?

      
   
                
               
      
A. A randomly selected person from Pollster A's population is more likely to weigh between 145 and 155 than Pollster B's population.
B. People in the population Pollster A surveyed are less alike in weight than those in the population surveyed by Pollster B.
C. The standard deviation of both populations is the same.
D. The standard error of both populations is the same.

Explanation / Answer

a) Clearly as the Margin of error for population A is larger than that of B, for a given interval, population B would be more confident that the weight is between 145 and 155 than poppulation A. Therefore this given statement is False:

b) Clearly as population A has a larger margin of error the population of A surveyed are less alike in weight than those in populaiton surveryed by B. Therefore the given statement is True.

c),d)

Standard deviation and standard error both will be greater for population A because it has a larger margin of error than population B. Therefore both c) and d) are false.

Therefore concluding remarks: Statement b) is the only correct statement.

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