Question

Organize the data into a two-by-two contingency table, with buses above and below the median of each variable. Determine whether the age of the bus is related to the amount of the maintenance cost. Use 0.05 significance level. (chi-saqure)

Median
Maint. Cost	4178.5
Age	7
Contingency Table (Observed)
	Old	New	Total
High Maint.	31	9	40
Low Maint.	7	33	40
Total	38	42	80

Answer 1

We first compute the expected value of each cell here as:

	Old	New
High Maintenance	40*38/80 = 19	40*42/80 = 21
Low Maintenance	40*38/80 = 19	40*42/80 = 21

The chi square test statistic now is computed from the given observed frequencies and expected frequencies computed above as:

Df = (num of col - 1)(num of row - 1) = 1

Therefore the p-value here is computed from the chi square distribution tables as:

As the p-value here is approx. 0, therefore the test is significant and we can conclude here that we have sufficient evidence that age of the bus is related to the amount of the maintenance cost