Question

1. City of Windhoek knows from past experience that 23% of the commuters in the city use their private cars, while 35% make use of busses, and the remaining 42% use taxis as a mode of transport to and from work, The Major of the City recently examined a random sample of 200 commuters and makes the following summary:
   

	Private Cars	bus	Taxi	Total
Number of commuters	37	47	116	200

1. Use the Chi square goodness of fit test to see if the preceding percentages fit these observations. Use α = 0.05
2. What should the Major conclude about the mode of transport for the city residents

Answer 1

Here ,

P(Private cars) = 0.23

P(Busses) =0.35

P(Taxis) = 0.42

Total commuters = 200

Expected commuters from private cars = 200 * 0.23 = 46

Expected commuters from Bus = 200 * 0.35 = 70

Expected commuters from Taxi = 200 * 0.42 = 84

Here value of chi-square value

=

= (37 - 46)²/46 + (47 - 70)²/70 + (116 - 84)²/84

= 21.51

Here degree of freedom = dF = n - 1 = 3 -1 = 2

critical value at 0.05 level = CHIINV(0.05, 2) = 5.9915

so here > (Critical)

so we would reject the null hypothesis and conclude that city of windhoek doesn't follow past precedence in the matter of mode of transport for the city residents.