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You have seen the χ 2 test statistic used in three different circumstances. The following bulleted list is a summary that will help you decide which χ 2 test is the appropriate one to use.

  • Goodness-of-Fit: Use the goodness-of-fit test to decide whether a population with an unknown distribution "fits" a known distribution. In this case there will be a single qualitative survey question or a single outcome of an experiment from a single population. Goodness-of-Fit is typically used to see if the population is uniform (all outcomes occur with equal frequency), the population is normal, or the population is the same as another population with a known distribution. The null and alternative hypotheses are:
    H 0 : The population fits the given distribution.
    H a : The population does not fit the given distribution.
  • Independence: Use the test for independence to decide whether two variables (factors) are independent or dependent. In this case there will be two qualitative survey questions or experiments and a contingency table will be constructed. The goal is to see if the two variables are unrelated (independent) or related (dependent). The null and alternative hypotheses are:
    H 0 : The two variables (factors) are independent.
    H a : The two variables (factors) are dependent.
  • Homogeneity: Use the test for homogeneity to decide if two populations with unknown distributions have the same distribution as each other. In this case there will be a single qualitative survey question or experiment given to two different populations. The null and alternative hypotheses are:
    H 0 : The two populations follow the same distribution.
    H a : The two populations have different distributions.

Chapter review

The goodness-of-fit test is typically used to determine if data fits a particular distribution. The test of independence makes use of a contingency table to determine the independence of two factors. The test for homogeneity determines whether two populations come from the same distribution, even if this distribution is unknown.

Which test do you use to decide whether an observed distribution is the same as an expected distribution?

a goodness-of-fit test

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What is the null hypothesis for the type of test from [link] ?

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Which test would you use to decide whether two factors have a relationship?

a test for independence

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Which test would you use to decide if two populations have the same distribution?

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How are tests of independence similar to tests for homogeneity?

Answers will vary. Sample answer: Tests of independence and tests for homogeneity both calculate the test statistic the same way ( i j ) ( O - E ) 2 E . In addition, all values must be greater than or equal to five.

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How are tests of independence different from tests for homogeneity?

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Bringing it together

  1. Explain why a goodness-of-fit test and a test of independence are generally right-tailed tests.
  2. If you did a left-tailed test, what would you be testing?
  1. The test statistic is always positive and if the expected and observed values are not close together, the test statistic is large and the null hypothesis will be rejected.
  2. Testing to see if the data fits the distribution “too well” or is too perfect.
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Questions & Answers

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is the branch of biology that deals with the study of microorganisms.
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studies of microbes
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they make spores
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Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
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Give Examples of thermophilic organisms
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Prevent foreign microbes to the host
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they provide healthier benefits to their hosts
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They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!
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cell is the smallest unit of life
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cell is the structural and functional unit of life
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is the fundamental units of Life
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part of a tissue or an organ being wounded or bruised.
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Binomial nomenclature
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Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
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