Question

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. Freshmen 83 Sophomores 68 Juniors 85 Seniors 64 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. The calculated value for the test statistic equals a. 6.66. b. 1.66. c. .54. d. .65. Icon Key

Answer 1

1.66

Explanation:

Using the Chi square statistic (χ²) test :

χ² = Σ(Oi - Ei)² / Ei

Expected, Ei :

Freshmen = 30% * 300 = 90

Sophomore =24% * 300 = 72

Junior = 26% * 300 = 78

Senior = 20% * 300 = 60

Observed, Oi :

Freshmen = 83

Sophomore = 68

Junior = 85

Senior = 64

χ² = ((83 - 90)²/90) + ((68 - 72)²/72) + ((85 - 78)²/78) + (64 - 60)²/60)

χ² = 49/90 + 16/72 + 49/78 + 16/60

χ² = 0.544 + 0.222 + 0.628 + 0.267

χ² = 1.661

The test statistic = 1.66