Question

The mayor of a large city claims that 25% of the families in the city earn more than $ 100,000 per year; 55% earn between $ 30,000 and $ 100,000 (inclusive); 20 % earn less than $ 30,000 per year. In order to test the mayor's claim, 285 families from the city are surveyed and it is found that: 80 of the families earn more than $ 100,000 per year; 140 of the families earn between $ 30,000 and $ 100,000 per year (inclusive); 65 of the families earn less $ 30,000. Test the mayor's claim based on 10 % significance level. BIVA-A- IEE311xx, E B. VCT 12pt Paragraph

Answer 1

Answer:
iven thalo Given 0 The Mayor of a large city claims that 25% of the families than $ 100.000 per year. No of feenildes = 285 in the city earen gore Niz 0.25 X 2857 = 11:25 55% and & 100,000 earen between $30,000 N 2 = 0.55 x 285 156,75 s 20 % caren less than $ 30.000 per year N3 = 0.20 X 285 s. 57 Now we can dest the Mayor's clary based on tot 10% søgnificance levele 10 50:1 100 for this Nel hypothermie Hos in this deetoeboete op &s same as Mayor's claim. In Alternative hypothesis His the distree bution defferent than what May is claim. Then, We can choose whell hypothesie Ho. ho

2 Observed value Expeeted value 80 11.25 Barenyengs More than $100,000 Between $30,000 and $109.000 Less than $30, 140 156. To 65 57 Test-statue Rož (observed to (observed in expected 12 Expected (90-71.25.)2+(140-156.760)2 + 165-51J? + 71.25 156.75 51 280.5625 351.5625 71.25 + t 64 5) 156.75 s 4.9342 +1.7898 + 1.12280 7.846 x² = 1084 Degree of freedom an-l 3-1 52 The søgne fecance level.4 = oil. Then, the create cay value at f = 0. l,df = 2 .5 4.605 [earn a2 table

3 statistic value We well Therefore, the test greater than the creetical value. Then reject the Ho.. nell hypothese Therefore the Mayor's elaim test based on 40%. sign of cance level des not scepported.