91Ó°ÊÓ

The City of South Lake Tahoe, CA, has an Asian population of $1,419$people, out of a total population of$23,609$.

To test these hypothesis:

$H_0$: The self-reported sub-groups of Asians in the Manhattan area fit that of the Lake Tahoe area

$H_1$: The self-reported sub-groups of Asians in the Manhattan area do not fit that of the Lake Tahoe area

Since there are $6$types of race, the nnumber of degrees of freedom is $6-1=5$.

We are using ${\mathrm{χ}}^2$distribution.

Test statistic is given by

${\mathrm{χ}}^2=\frac{(131-174{)}^2}{131}+\frac{(118-557{)}^2}{118}+\frac{(1045-518{)}^2}{1045}++\frac{(80-54{)}^2}{80}+\frac{(12-29{)}^2}{12}+\frac{(9-21{)}^2}{9}+\frac{(24-66{)}^2}{24}$

$=14.1+1633.23+265.77+8.45+24.083+16+73.5$

$=2035.146$

Using the applet, we get that $p$-value is $0$:

Taking $\mathrm{Î\pm }=0.05$, we can see that

This means that we reject null hypothesis. There is evidence to conclude that the sub-groups of Asians in the Manhattan area do not fit that of the Lake Tahoe area.