Question

A recent census report indicated the following percentages for methods of commuting to work for workers over 15 years of age: 76.6% drive alone, 9.7% carpool, 4.9% use public transportation, 2.8% walk, 1.7% use other forms of transportation, 4.3% work at home. A random sample of workers yielded the following table of observed methods of commuting to work.

Method	Alone	Carpool	Public	Walk	Other	Home
Observed	355	65	30	20	10	20

Is there sufficient evidence to conclude that the percentages of workers using each type of transportation differ from those in the census report? Compute the test statistic value for this test.

Answer 1

The expected frequency is first obtained here as:

E_i = p_i* Total Frequency

These are computed here as:

Method	O_i	E_i	(E_i - O_i)^2/E_i
Alone	355	383	2.047
Carpool	65	48.5	5.613
Public	30	24.5	1.235
Walk	20	14	2.571
Other	10	8.5	0.265
Home	20	21.5	0.105
	500	500	11.836

The chi square test statistic here is computed (using the computations in the last column) here as:

Therefore 11.836 is the test statistic value for the test here.

For n - 1 = 6 - 1 = 5 degrees of freedom, the p-value here is computed from the chi square distribution tables as:

As the p-value here is 0.04 < 0.05 which is the level of significance here. Therefore the test is significant here and we can reject the null hypothesis here and conclude that he percentages of workers using each type of transportation differ from those in the census report at the 5% level of significance.