I've ran into a few problems that use different formulas to compute the z score. Some solutions show z = (observation - population mean)/ standard deviationSome 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?

Make sure you get the probability for LEFT outter portion of tail. For example 2.5% on a z value of 1.96

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.

A CFA Level 1 Discussion About Z Scores.

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This topic has 4 replies, 2 voices, and was last updated Apr-1812:05 am by googs1484.

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- emmanuel.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?
- googs1484
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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
- googs1484
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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.
- googs1484
  Participant
  - 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.
- googs1484
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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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