1 answer

A particular city has an Asian population of 1419 people, out of a total population of...

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.


Answers

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
.

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