Question

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 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 400 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 her hypothesis?

   Defective

Day Car Made Monday   Other Days

      No 26 142

     Yes 68 162

Answer 1

Answer

we have to test whether people are more likely to make more defects on mondays or not.

Null hypothesis

Ho: Hmonday Hother days

Alternate hypothesis

Ha . Įlm onday > μ。t her days

Using TI 84 calculator

press 2nd then matric, then enter data into matrix A

press stats then tests then alpha c

select matrix A as observed values and matrix B as expected values, press enter

we get

chi-square statistic = 10.68

p value = 0.0011

it is clear that p value is less than 0.05 significance level, so rejecting the null hypothesis

we can conclude that there are more defects on monday as compared to other days based on the chi-square test result