The City of South Lake Tahoe, CA, has an Asian population of 1,419 people, out of a total population of 23,609. Suppose that a survey of 1,419 self-reported Asians in the Manhattan, NY, area yielded the data in the table below. Conduct a goodness-of-fit test to determine if the self-reported sub-groups of Asians in the Manhattan area fit that of the Lake Tahoe area.

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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  • The City of South Lake Tahoe, CA, has an Asian population of 1,419 people, out of a total population of 23,609. Suppose that a survey of 1,419 self-reported Asians in the Manhattan, NY, area yielded the data in the table below. Conduct a goodness-of-fit test to determine if the self-reported sub-groups of Asians in the Manhattan area fit that of the Lake Tahoe area. 

 

Race

Lake Tahoe Frequency

Manhattan Frequency

Asian Indian

131

174

Chinese

118

557

Filipino

1045

518

Japanese

80

54

Korean

12

29

Vietnamese

9

21

Other

24

66



  • H0 : _______
  • Ha :  _______
  • What are the degrees of freedom?
  • State the distribution to use for the test.
  • What is the test statistic?
  • What is the p-value? In one to two complete sentences, explain what the p-value means for this problem.
  1. Use the previous information to sketch a picture of this situation. Clearly label and scale the horizontal axis and shade the region(s) corresponding to the p-value.
    1. Indicate the correct decision (“reject” or “do not reject” the null hypothesis) and write appropriate conclusions, using complete sentences.
  • Alpha: _______
  • Decision: _______
  • Reason for decision: _______
  • Conclusion: _______

 

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