Question

mandrake falls high school is providing a weekend course in laboratory techniques to its laboratory students. of the 200 students enrolled in lab classes at mandrake, 78 have taken the weekend course. mandrake is evaluating the course’s effectiveness by having its lab instructors record harmful lab “incidents”: students, misuse of lab equipment, etc. the contingency table below gives a summary of the data that have been gathered so far for the 200 lab students. each student is classified according to two variables: status regarding lab techniques course (“took the course” or “didn’t take the course”) and laboratory performance (“involved in no incident”, “involved in exactly one incident”, or “involved in 2+ incidents”). in the cells of the table are the respective observed frequencies. note that three of the cells also have blanks. fill in these blanks with the frequencies expected if the two variables, status regarding lab techniques course and laboratory performance, are independent. round your answers to two or more decimal places.

status regarding lab techniques course	laboratory performance
	took the techniques course	37	28	13	78
		blank	blank	blank
	didn’t take the techniques course	68	34	20	122
		blank	blank	blank
total		105	62	33	200

Explanation:

Step1: Calculate expected frequency formula

Expected frequency = $\frac{\text{Row Total} \times \text{Column Total}}{\text{Grand Total}}$

Step2: Compute Took course - No incident

$\frac{78 \times 105}{200} = \frac{8190}{200} = 40.95$

Step3: Compute Took course - 2+ incidents

$\frac{78 \times 33}{200} = \frac{2574}{200} = 12.87$

Step4: Compute Didn't take course - 2+ incidents

$\frac{122 \times 33}{200} = \frac{4026}{200} = 20.13$

Answer:

Took the techniques course - Involved in no incident: 40.95
Took the techniques course - Involved in 2+ incidents: 12.87
Didn't take the techniques course - Involved in 2+ incidents: 20.13