Lemon Corporation, an automobile manufacturer, is trying to determine the source of defects in some of its autos. Rumor has it that on Mondays large numbers of Lemon auto workers are hung over from a weekend of drunkenness and debauchery and are, therefore, more likely to make mistakes on the job. In order to test the hypothesis of more defects on Mondays, the company draws a random sample of 200 automobiles made by Lemon in the last two years. In this sample, they cross-tabulate the day the auto was made (Monday vs. all other days) with the variable of whether or not the care has any known defect. Based on the data below, is there support for the rumored hypothesis?
Day Car Made
Defect Monday Other Days Total
No 10 78 88
Yes 29 83 112
Total 39 161 200
Null hypothesis: the defect of the car is independent from the day the auto was made.
Alternative hypothesis: the defect of the car is associated with the day the auto was made.
The solution provides detailed explanation how to perform the chi square test.