15. A researcher wants to be sure that the sample in her study is not unrepresentative of the distribution of ethnic groups in her community. Her sample includes 300 whites, 80 African Americans, 100 Latinos, 40 Asians, and 80 others.

In her community, according to census records, there are 48% whites, 12%

African Americans, 18% Latinos, 9% Asians, and 13% others. Is her sample unrepresentative of the population in her community? (Use the .05 level.)

(a) Carry out the steps of hypothesis testing.

(b) Make a sketch of the distribution involved.

(c) Explain your answer to a person who has never taken a course in statistics. (This problem is a chi-square for a single nominal variable;

it is not a chi-square test for independence and does not involve any contingency tables.)