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 129
Chinese 119
Filipino 1041
Japanese 85
Korean 14
Vietnamese 10
Other 21
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.