Question

At the end of a semester, the students’ grades for Business Data Analysis 1 were tabulated in the following 3×2 contingency table to see if there is any association between class attendance and grades received

# of Days Absent Grade Received Pass Fail 0-3 135 110 4-6 36 4 7-25 9 6

(a) Calculate the probability that a student selected at random:

i. Was absent for less than four days

ii. Was absent for less than seven days

iii. Passed iv. Passed given that he/she was absent for less than four days

v. Passed or was absent for less than four days

vi. Passed and was absent for less than four days. (b) Calculate the expected value for the number of days absence (c) Calculate the 95% confidence intervals for the

i. Percentage of students who passed

ii. Percentage of them who failed

iii. Interpret your findings

Answer 1

The given information is,

	0-3	4-6	7-25	Total
Pass	135	36	9	180
Fail	110	4	6	120
Total	245	40	15	300

(a)

i. P(Student absent less than 4 days)

ii. P(Student absent for less than 7 days)

Means for both 0 - 3 as well as 4 - 6

iii. P(Student passed)

iv. P(Pass given he/she was absent for less than four days)

v. P(Passed or absent for less than four days)

vi. P(Passed and was absent for less than four days)

(b) Expected values for the number of days absence

The expected value for passed and less than 3 days absent

The expected value for passed and absent between 4 to 6 days

The expected value for passed and absent between 7 to 25 days

The expected value for Fail and less than 3 days absent

The expected value for Fail and absent between 4 to 6 days

The expected value for Fail and absent between 7 to 25 days

(c) 95% confidence intervals

i. For the percentage of student who passed

The formula to find the confidence interval is,

To find Z, first, find alpha which is 1 - c = 0.05

alpha/2 = 0.025, 1 - (alpha/2) = 0.975

By using z table the Z critical value for area 0.975 is 1.96

Z = 1.96

Plugging all values in the formula of confidence interval is,

(0.5446, 0.6554)

ii. Confidence interval for proportion of student who failed

The formula to find the confidence interval is,

The critical value is the same as 1.96

(0.3446, 0.4554)

iii. We are 95% confident that the true proportion of student who passed is lies between 0.5446 and 0.6554

Also, we are 95% confident that the true proportion of student who failed is lies between 0.3446 and 0.4554