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A sample is obtained from a population with m = 100 and s = 20. Which of the following samples would produce the most extreme z-score? A sample of n = 25 scores with M = 102 A sample of n = 100 scores with M = 102 A sample of n = 25 scores with M = 104 A sample of n = 100 scores with M = 104

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Answer:

A sample of n = 100 scores with M = 104 gives the most extreme z-score.

Step-by-step explanation:

The difference between sample mean and population mean is (Standard Error of the Mean) can be written by the formula

SE=(M-m)=[tex]\frac{z*s}{\sqrt{n}}[/tex] where M is the sample mean, m is the population mean, z is the z-score, s is the population standard deviation, n is the size of the sample. From this we can find out that

z=(M-m)×[tex]\frac{\sqrt{n} }{s}[/tex]

[tex]\\[/tex]

  • A sample of n = 25 scores with M = 102 gives

       z=(102-100)×[tex]\frac{\sqrt{25} }{20}[/tex] =0.5

  • A sample of n = 100 scores with M = 102 gives

        z=(102-100)×[tex]\frac{\sqrt{100} }{20}[/tex] =1

  • A sample of n = 25 scores with M = 104 gives

        z=(104-100)×[tex]\frac{\sqrt{25} }{20}[/tex] =1

  • A sample of n = 100 scores with M = 104 gives

        z=(104-100)×[tex]\frac{\sqrt{100} }{20}[/tex] =2

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