The following data represent the level of happiness and level of health for a random sample of individuals from the General Social Survey. A researcher wants to determine whether health and happiness level are related. Test the researcher's claim at the αα = 0.05 level of significance.                                Health     Excellent Good Fair Poor Happiness Very Happy 271 261 82 20 Pretty Happy 247 567 231 53 Not Too Happy 33 103 92 36                 *Source: General Social Survey Determine the null and alternative hypotheses. H0: Health and happiness have the same distribution. Ha: Health and happiness follow a different distribution. H0:Health and happiness are independent. Ha: Health and happiness are dependent. Determine the χ2 test statistic. Round to two decimal places. χ2 =  Determine the pp-value. Round to four decimal places. p-value =    Make a conclusion. There is sufficient evidence to support the claim that health and happiness are related. There is not sufficient evidence to support the claim that health and happiness are related.

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The following data represent the level of happiness and level of health for a random sample of individuals from the General Social Survey. A researcher wants to determine whether health and happiness level are related. Test the researcher's claim at the αα = 0.05 level of significance.                           

    Health
    Excellent Good Fair Poor
Happiness
Very Happy 271 261 82 20
Pretty Happy 247 567 231 53
Not Too Happy 33 103 92 36

               

*Source: General Social Survey

Determine the null and alternative hypotheses.

  • H0: Health and happiness have the same distribution.
    Ha: Health and happiness follow a different distribution.
  • H0:Health and happiness are independent.
    Ha: Health and happiness are dependent.



  1. Determine the χ2 test statistic. Round to two decimal places.
    χ2 = 

  2. Determine the pp-value. Round to four decimal places.
    p-value = 

    •  


  3. Make a conclusion.
    • There is sufficient evidence to support the claim that health and happiness are related.
    • There is not sufficient evidence to support the claim that health and happiness are related.
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