Exhibit 12-2 Last school year, the student body of a local university consisted

Question

Exhibit 12-2
Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.

We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year.

Refer to Exhibit 12-2. The calculated value for the test statistic equals

0.5444

300

1.6615

6.6615

Freshmen 83 Sophomores 68 Juniors 85 Seniors 64

Explanation / Answer

Check for assumptions:

Counted data: There are counts of students in each classification.

Independence assumption: the students are independent of each other.

Randomization condition: the students are though not a random sample, but they are representative of the college population past and future.

10% condition:; these 300 students are less than 10% of the population of all college students in the given category in current year.

Expected cell frequency: expected cell frequency (computed below) is atleast 5.

This accounts for Chi-square Goodness of fit test. Compute the test statistic as follows:

X^2=sigma (Observed-Expected)^2/Expected

=1.66154

~1.6615 (ans)

Ans. C

Observed value, fo Proportion, pi Expected value, fe=N*pi (Observed-Expected)^2/Expected 83 0.30 90 0.544444 [(83-90)^2/90] 68 0.24 72 0.222222 85 0.26 78 0.628205 64 0.20 60 0.266667 Total, N=300

X^2=sigma (Observed-Expected)^2/Expected

=1.66154

~1.6615 (ans)

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.