Hypothesis Testing

So far, we have discussed ways to describe our distributions. We want to continue this discussion in a slightly different way.  Now, we want to talk about hypothesis testing.  In hypothesis testing we want to determine whether a newly collected data belongs to a given distribution.  There are four possible answers to this question:

  1. The data value is part of the population of data values that makes up the distribution.
  2. The data value is not part of the population of data values that makes up the distribution, but fits the distribution due to random sampling.
  3. The data value is not part of the population of data values that makes up the distribution and does not fit the distribution.
  4. The data value is part of the population but does not fit the distribution due to random variance around the mean.
In hypothesis testing, we use two different hypotheses, the null hypothesis and the alternative hypothesis.  For our purposes, we will use the following definitions of the two hypotheses:
  • The null hypothesis states that any difference between the test data value and the distribution is due to normal variation (random sampling).
     
  • The alternative hypothesis states that the difference between the test data value and distribution is due to a significant difference in the distribution and test data value (meaning that the data value is not truely a member of the distribution).
    Quick Quiz: State the null hypothesis for the following case: The average N2O concentration is 315 (nL / L).
    The sampling mean is greater than 315
    The sampling mean is equal to 315
    The sampling mean is less than 315
    None of the above

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