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z scores.

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    • Avatar of emmanuel.chemmanuel.ch
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        • Undecided
        26 Apr 2018 at 9:50 am
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        I’ve ran into a few problems that use different formulas to compute the z score. 

        Some solutions show z = (observation – population mean)/ standard deviation

        Some solutions show z = (observation – population mean)/(Std error) 
        where std error = (std deviation/Sqrt(population size))

        the following question used the second equation to compute the z score while I used the first equation [(z = observation – population mean)/ std deviation]

         How would I know which one to use? they gave significantly different answers.

        Please refer to question B. I am fine with question A. 

        Ex: Assume that the equity risk premium is normally distributed with a population mean of 6% and a population std. deviation of 18%. Over the last four years, equity returns (relative to the risk free rate) have averaged -2.0%. You have a large client who is very upset and claims that results this poor should never occur. Evaluate your client’s concerns. 
        A. Construct a 95% confidence interval around the population mean for a sample of four year returns. 
        B. What is the probability of a -2.0 percent or lower average return over a four year period? 

      • Avatar of googs1484googs1484
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          • CFA Level 3
          26 Apr 2018 at 11:56 pm
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          Make sure you get the probability for LEFT outter portion of tail. For example 2.5% on a z value of 1.96

        • Avatar of googs1484googs1484
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            • CFA Level 3
            26 Apr 2018 at 11:55 pm
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            Your not testing the hypothesis of a SAMPLE here. 95% confidence interval is 1.96 plus/minus 6 percent. The probability of would be (-.02 – .06)/.18. Take that value and look it up on z table.

          • Avatar of googs1484googs1484
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              • CFA Level 3
              27 Apr 2018 at 12:00 am
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              Some solutions show z = (observation – population mean)/(Std error) 
              where std error = (std deviation/Sqrt(population size))

              Hint: use this one when you see a sample size in the question. Only use this hint if you’re really strapped on time though. Could throw a curveball obviously on the test. 

            • Avatar of googs1484googs1484
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                • CFA Level 3
                27 Apr 2018 at 12:05 am
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                googs1484 said:
                Your not testing the hypothesis of a SAMPLE here. 95% confidence interval is 1.96 plus/minus 6 percent. The probability of would be (-.02 – .06)/.18. Take that value and look it up on z table.

                Oops sry this was wrong but I’m hoping you caught it. Forgot to multiply 1.96 by 18 percent 

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