Question

Public officials for the city of San Francisco, California, have questioned the accuracy of the year 2000 national census. An SRS of 1000 city residents was used to check the percentage of different ethnic groups living in San Francisco. The pertinent data are given in the table below.

Ethnic Origin            Census Percent                      Observed frequency from sample

Asian                             30%                                                  290

Black                             10%                                                  65

Latino                             35%                                                  400

Native American              5%                                                    30

Anglo                              15%                                                  160

Other                               5%                                                    55

Use the significance level of 0.05 to test the accuracy of the year 2000 census regarding the different ethnic groups.

Answer 1

null hypothesis:Ho:  distribution of different ethnic groups living in San Francisco is same as cesus 2000

alternate hypothesis:Ha:distribution of different ethnic groups living in San Francisco is different from cesus 2000

degree of freedom =groups-1=6-1=5

for 5 df and 0.05 level critcal value =11.070

applying chi square goodness of fit test:

		observed	Expected		Chi square
category	Probability(p)	Oi	Ei=total*p		R2i=(Oi-Ei)2/Ei
Asian	0.300	290.000	300.00		0.333
Black	0.100	65.000	100.00		12.250
Latino	0.350	400.000	350.00		7.143
Native American	0.050	30.000	50.00		8.00
Anglo	0.150	160.000	150.00		0.67
Other	0.050	55.000	50.00		0.50
total	1.000	1000	1000		28.89

here as test statistic 28.89 is higher than critical value we reject null hypothesis

we have sufficient evidence to conclude at 0.05 level that   accuracy of the year 2000 census regarding the different ethnic groups is doubtful