Question

The number of AIDS cases reported for Santa Clara County, California is broken down by race in the table below. Source: "HIV/AIDS Epidemiology Santa Clara County", Santa Clara County Public Health Department, May 2011.

Race	Cases
White	2310
Hispanic	1144
Black	451
Asian/Pacific Islander	240
Total	4145

Directions: Conduct a chi-square test for goodness-of-fit to determine whether or not the occurrence of AIDS cases is consistent with the race distribution of Santa Clara County.

1. Choose the correct null and alternative hypotheses.
   • H0:H0: The distribution of AIDS cases is consistent with the race distribution in Santa Clara County.
     HaHa The distribution of AIDS cases is different from the race distribution in Santa Clara County.
   • H0H0 The distribution of AIDS cases is different from the race distribution in Santa Clara County.
     Ha:Ha: The distribution of AIDS cases is consistent with the race distribution in Santa Clara County.
2. Compute the test statistic.
   
   The population distribution of Santa Clara County by race is provided in the table below. Use these percentages to compute the expected number of cases for each racial group. Round each of the expected counts to 2 decimal places.
   

   Race	Proportion	Expected cases
   White	0.411
   Hispanic	0.276
   Black	0.027
   Asian/Pacific Islander	0.286
   Total	1

   
   Determine the value of the test statistic. Round your answer to 1 decimal place.
   
   χ2=χ2=
   
3. Compute the p-value. Round your answer to 4 decimal places.
   
   p-value =

Answer 1

The statistical software output for this problem is:

Hence,

Hypotheses:

H0: The distribution of AIDS cases is consistent with the race distribution in Santa Clara County.
Ha The distribution of AIDS cases is different from the race distribution in Santa Clara County.

Race	Proportion	Expected cases
White	0.411	1703.60
Hispanic	0.276	1144.02
Black	0.027	111.92
Asian/Pacific Islander	0.286	1185.47
Total	1

Test statistic = 1997.3

p - Value = 0.0000