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 135 202.71 chinese 123 202.71 filipino 1038 202.71 japanese 76 202.71 korean 14 202.71 vietnamese 10 202.71 other 23 202.71 part (a) state the null hypothesis. the self-reported sub-groups of asians are evenly distributed. the self-reported sub-groups of asians are not evenly distributed.

Answer 1

To conduct a goodness of fit test at the 5% level, compare the observed frequencies with the expected frequencies to determine if the self-reported sub-groups of Asians are evenly distributed.

Step-by-step explanation:

To conduct a goodness of fit test at the 5% level, we need to compare the observed frequencies with the expected frequencies. The null hypothesis is that the self-reported sub-groups of Asians are evenly distributed. The alternative hypothesis is that the self-reported sub-groups of Asians are not evenly distributed.

1. Calculate the expected frequency for each sub-group by multiplying the proportion of Asians in the total population by the total number of Asians.
2. Calculate the chi-square test statistic using the formula: ∑((observed frequency - expected frequency)^2 / expected frequency).
3. Compare the calculated chi-square test statistic with the critical value from the chi-square distribution table at a significance level of 0.05.
4. If the calculated chi-square test statistic is greater than the critical value, reject the null hypothesis and conclude that the self-reported sub-groups of Asians are not evenly distributed. If the calculated chi-square test statistic is less than or equal to the critical value, fail to reject the null hypothesis and conclude that the self-reported sub-groups of Asians are evenly distributed.

Answer 2

Given that a particular city has an asian population of 1419 people, out of a total population of 23,609.

To conduct a goodness of fit test at the 5% level to determine if the self-reported sub-groups of asians are evenly distributed.

Since, the parameter of interest is 'if the self-reported sub-groups of asians are evenly distributed', thus the null hypothesis is "the self-reported sub-groups of asians are evenly distributed".