Question

An instructor is interested in seeing if there is an association between attendance and final grade earned in a freshman level class. He records the number of absences for each student and then whether they pass or fail the class. The results are summarized below.

Number of Absences

	0-3	4-6	7+	Total
Total	135	66	29	230
Fail	28	19	23	70
Total	163	85	52	300

Construct a 99% confidence interval for the true proportion of students who pass the class Round your sample statistic and confidence limits to three decimal places.
0.
1.
2.

3.

4.

5.

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b. At a 0.01 significance level, can the instructor conclude that there is a relationship between number of absences and whether the student passes or fails the class? (Note: Round expected counts to the nearest whole number)
1.
2.
3.
4.
5.

Answer 1

Answer:

(a)

Step 1:

n = Sample Size = 300

= Sample Proportion = 230/300 = 0.767

Step 2:

= 0.01

From Table, critical values of Z = 2.576

Step 3:

Confidence Interval:

So,

Answer is:

(0.704, 0.830)

(b)

Step !

H0: Null Hypothesis: There is no relationship between number of absentees and whether the student passes or fails the class.

HA: Alternative Hypothesis: There is a relationship between number of absentees and whether the student passes or fails the class.

Step 2:

Expected Frequencies are got as follows (AS REQUIRED IN THE QUESTION: Round expected counts to the nearest whole number):;

	0-3	4-6	7+	Total
Pass	163 X 230/ 300 = 125	85 X 230/ 300 = 65	52 X 230/ 300 = 40	230
Fail	163 X 70/ 300 = 38	85 X 70/ 300 = 20	52 X 70/ 300 = 12	70
Total	163	85	52	300

Step 3:

Test Statistic () is got as follows:

Observed (O)	Expected (E)	(O - E)2/E
135	125	0.800
66	65	0.015
29	40	3.025
28	38	2.632
19	20	0.050
23	12	10.083
Total = =		16.605

Step 4:

= 0.01

df = (r - 1) X (c - 1) = (2 - 1) X (3 - 1) = 2

From Table, critical value of = 9.2103

Since calculated value of = 16.605 is greatr than critical value of = 9.2103, the difference is significant. Reject null hypothesis.

Conclusion:
The data supports the claim that there is a relationship between number of absentees and whether the student passes or fails the class.

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