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  ```One-Sample t-test
  What do these problems we have been working on have in
  common?
  In a population of American graduate students, individuals
  earn on average \$7.25/hour on alcohol, with a standard
  students from Brooklyn earn a different wage than grad
  students in general. I gather together 9 graduate students
  from this program and calculate the average amount they
  earn an hour: \$11.00. Use an alpha level of .01.
  How do I know I need to be using a z-test?
  1. We are comparing a sample mean to a KNOWN population mean.
  2. We KNOW the population s.
  What to do if you do not know the Population
  Standard Deviation (s)?
  Use the best estimate of sx
  You must correct for the
  uncertainty of this estimate.
  T-score for a single sample mean
  Where sx_ =
  s
  What to do if you do not know the Population
  Standard Deviation (s)?
  _
  x
  _
  x
  Probability
  Hypothesis testing with the t-statistic
  Retain H0
  Outcome âtâ
  Reject H0
  t-crit
  One-tailed test
  One-Sample t-test
  z-test is used when we know both m and s
  t-test is when we know m but not s
  The Sampling Distribution of the t-test
  This table lists the critical value of the t-statistic for the
  Degrees of freedom and a level.
  Given the level and the df you can find the critical value
  of the t-statistic that divides the outcomes into reject or retain the null.
  The average IQ score of Americans is 100. I believe that my Statistics
  class (you guys!) have different IQs than the general population. I force
  all 15 of you to take an IQ test, and I calculate a mean of 110 (s= 20). Use
  an alpha level of .05 to determine if this class has a different IQ than the
  population.
  How do I know I need to be using a one-sample t-test?
  Step 1: State the null and alternative hypotheses:
  H0: My stats class does not have a different IQ than the average American
  H1: My stats class has a different IQ than the average American
  Step 2: Find the critical value.
  Go to t-table! Must figure out of this is one- or two-tailed, and df.
  The Sampling Distribution of the t-test
  This table lists the critical value of the t-statistic for the
  Degrees of freedom and a level.
  Given the level and the df you can find the critical value
  of the t-statistic that divides the outcomes into reject or retain the null.
  The average IQ score of Americans is 100. I believe that my Statistics
  class (you guys!) have different IQs than the general population. I force
  all 15 of you to take an IQ test, and I calculate a mean of 110 (s= 20). Use
  an alpha level of .05 to determine if this class has a different IQ than the
  population.
  How do I know I need to be using a one-sample t-test?
  Step 1: State the null and alternative hypotheses:
  H0: My stats class does not have a different IQ than the average American
  H1: My stats class has a different IQ than the average American
  Step 2: Find the critical value.
  Go to t-table! Must figure out of this is one- or two-tailed, and df.
  +/-2.145
  The average IQ score of Americans is 100. I believe that my Statistics
  class (you guys!) have different IQs than the general population. I force
  all 15 of you to take an IQ test, and I calculate a mean of 110 (s= 20). Use
  an alpha level of .05 to determine if this class has a different IQ than the
  population.
  Step 3: Calculate the obtained statistic:
  tobt ï½
  x ï­ mx
  sx
  =
  - 100
  110
  ________
  = 10/5.17 = 1.93
  20/sqrt(15)
  Step 4: Make a decision.
  I
  I
  -2.15
  2.15
  Step 4: Retain the null hypothesis.
  The Sampling Distribution of the t-test
  This table lists the critical value of the t-statistic for the
  Degrees of freedom and a level.
  Given the level and the df you can find the critical value
  of the t-statistic that divides the outcomes into reject or retain the null.
  ```
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