OneSample z Test

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One-Sample z Test
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Population and Parameters
A Normally Distributed Population with a Mean of
0 and a Standard Deviation of 1
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Sample Size
n 100
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Form a Sampling Distribution of the Mean

• Draw all possible samples ofsize 100
• Compute the Sample Means

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Mean and Standard Error of the Mean

• The Mean of the Sampling Distribution of the Mean
  0
• The Standard Error of the Mean 1 / 10 .1

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Select a Random Sample

• Sample Size 100
• Sample Mean .27

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What is the probability of obtaining a sample
mean of .27 or more by chance?
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Locate the obtained sample mean of .27 in the
theoretical sampling distribution of all possible
sample means
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Form a z Ratio
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Probability
The probability above the z score of 2.7 is
.0037.
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Does a random sample mean of .27 come from a
population with a mean higher than 0?
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Hypotheses
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(No Transcript)
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Probability
Fewer than 4 of the sample means would deviate
this much and more from the expected mean of 0.
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Significance Level
The probability that defines samples as unlikely
is usually  
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Conclusion

• The probability of obtaining by chance a sample
  mean of .27 or more is smaller than .05.
• It is unlikely that the random sample is
  representative of the population with a mean of
  0.
• The random sample mean of .27 come from a
  population with a mean higher than 0.  

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Risk
p ? The probability of incorrectly rejecting
the null hypothesis that the mean of the
population is equal to 0 is .05.