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Quant - Level 1

EQ_ArbitrageEQ_Arbitrage United StatesPosts: 8 Associate
When constructing confidence intervals, how do you know when to multiply the standard error of the sample mean with the sample statistic, or to just multiply the the sample statistic by just the standard deviation?


2.5 ± 2.093(st. dev)
 or 

2.5 ± 2.093(std/ √n)

Comments

  • mvibsmvibs ColoradoPosts: 12 Associate
    there the key is in how they ask the question. Are they asking for a range, or test statistics to compare it to and reject or accept a hypothesis?

    Lets make ale it easy and assume mean of 5, std dev of 10. 

    1) what interval can you assume 90% of the samples will fall between?

    we know that 90% fall within 1.645 std dev of the mean. So multiply 10 by 1.645 to get 16.45. Answer will be 5 plus or minus 16.45 (-11.5 - 21.45)

    i would strongly recommend memorizing 90, 95 and 99% as well as that 68% fall within one standard deviation of the mean. 


    2) there are 25 samples drawn with a mean of 10. John wants to test his hypothesis that the mean is greater than 8.  Now you need to use a test statistic. I don't have them in front of me so I can't give you an example here. 


    hope this helps. 
  • Use the test statistic when the they mention a hypothesized value or test.  Also, the test statistic is when comparing sample statistic to a hypothesized value. 
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