$36.$ In studying the occurrence of some characteristics, the following sample data were obtained. Is there any

evidence that the proportions of each characteristic are different? What are the test statistic and p$-$value

for the most appropriate test? Use a $10\%$ level of significance.

Characteristics A B C

Frequency $303039$

a$)$ TS $=1\mathrm{.}64$; p$-$value $<0\mathrm{.}1.$

b$)$ TS $=1\mathrm{.}64$; p$-$value $>0\mathrm{.}1.$

c$)$ TS $=132\mathrm{.}0$; p$-$value $<0\mathrm{.}005.$

d$)$ TS $=132\mathrm{.}0$; p$-$value $>0\mathrm{.}005.$

e$)$ TS $=132\mathrm{.}0$; $0\mathrm{.}01<$ p$-$value $<0\mathrm{.}025.$