Question

A particular city has an Asian population of 1419 people, out of a total population of 23,609. Conduct a goodness of fit test at the 5% level to determine if the self-reported sub-groups of Asians are evenly distributed. Round expected frequency to two decimal places.

Race	Frequency	Expected Frequency
Asian Indian	134
Chinese	123
Filipino	1033
Japanese	83
Korean	13
Vietnamese	11
Other	22

• Part (a)

  State the null hypothesis.

  The self-reported sub-groups of Asians are not evenly distributed.The self-reported sub-groups of Asians are evenly distributed.    

• Part (b)

  State the alternative hypothesis.

  The self-reported sub-groups of Asians are evenly distributed.The self-reported sub-groups of Asians are not evenly distributed.    

• Part (c)

  What are the degrees of freedom?

• Part (d)

  State the distribution to use for the test.    

  t₆

  t₇

• Part (e)

  What is the test statistic? (Round your answer to two decimal places.)

• Part (f)

  What is the p-value? (Round your answer to four decimal places.)
  
  
  Explain what the p-value means for this problem.If

  H₀

  is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.If

  H₀

  is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value.    If

  H₀

  is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.If

  H₀

  is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value.

• Part (g)

  Sketch a picture of this situation. Label and scale the horizontal axis, and shade the region(s) corresponding to the p-value. (Upload your file below.)

• Part (h)

  Indicate the correct decision ("reject" or "do not reject" the null hypothesis) and write the appropriate conclusion.(i) Alpha:
  α =
  
  (ii) Decision:

  reject the null hypothesisdo not reject the null hypothesis    

  
  (iii) Reason for decision:

  Since α > p-value, we reject the null hypothesis.Since α > p-value, we do not reject the null hypothesis.    Since α < p-value, we reject the null hypothesis.Since α < p-value, we do not reject the null hypothesis.

  
  (iv) Conclusion:

  There is sufficient evidence to conclude that the self-reported sub-groups of Asians are not evenly distributed.There is not sufficient evidence to conclude that the self-reported sub-groups of Asians are not evenly distributed.

Answer 1

Given that:

Ho : Asians = not evenly distributed

Ha : Asians != not evenly distributed

df = 6	N = 1419
Race	Frequency(O)	Expected Frequency(E)	O-E	(O-E)^2	(O-E)^2/E
Asian Indian	134	202.7142857	-68.7143	4721.653061	23.29215745
Chinese	123	202.7142857	-79.7143	6354.367347	31.34642102
Filipino	1033	202.7142857	830.2857	689374.3673	3400.719219
Japanese	83	202.7142857	-119.714	14331.5102	70.69807712
Korean	13	202.7142857	-189.714	35991.5102	177.5479714
Vietnamese	11	202.7142857	-191.714	36754.36735	181.3111849
Other	22	202.7142857	-180.714	32657.65306	161.1018826
				Test Stastics	4046.016913
p value	0

P value is < 0.0001