Question

A retired statistician has taken a part time job as a kindergarten teacher. After her orientation training, she was happy to get her own classroom. She stocked her crayon boxes with colors she predicts the children will use most frequently based on her experience during orientation with a class of 30 children. She predicted that 58% would choose primary colors, 30% would choose secondary colors, and 12% would choose other colors.

	Primary	secondary	other
Observe frequency	212	112	79

Using a 0.05 significance level, test the claim that the actual frequencies correspond to her predicted distribu- tion. What is the value of the test statistic that would be used to test this hypothesis?
(a) 3.69
(b) 16.74
(c) 48.36
(d) 61.28
(e) 22.09

Answer 1

Answer)

Formula for test statistics is

Sum of (observed - expected)^2/expected

Observed for primary = 212

Expected for primary = 58% that is 58% of (212+112+79) = 0.58*403 = 233.74

Similarly, observed for secondary = 112, expected = 30% of 403 = 120.9

Observed for other = 79, expectes = 12% of 403 = 48.36

Test statistics = (212-233.74)^2/233.74 + (112-120.9)^2/120.9 + (79-48.36)^2/48.36

Test statistics = 2.022022760331 + 0.655169561621 + 19.412936311000

= 22.090128632952

= 22.09