Question

A developmental psychologist would like to determine whether infants display any color preferences. A stimulus consisting of four color patches (red, green, blue, and yellow) is projected onto the ceiling above a crib. Infants are placed in the crib, one at a time, and the psychologist records how much time each infant spends looking at each of the four colors. The color that receives the most attention during a 100-second test period is identified as the preferred color for that infant. The preferred colors for a sample of 60 infants are shown in the following table:

Red Green Blue Yellow
20 12 18 10
a. Do the data indicate any significant preferences among the four colors? Test at the .05 level of significance.
b. Write a sentence demonstrating how the outcome of the hypothesis test would appear in a research report.

Answer 1

There is insufficient evidence to suggest that preference exists among the four colors.

Explanation:

Xobserved, Xo = 20 __ 12 __ 18 __ 10

Xexpected, Xe = ΣX observed / n = 60 /4 = 15

Test statistic :

χ² = Σ(Xo - Xe)² / Xe

χ² = (20-15)²/15 + (12-15)²/15 + (18-15)²/15 + (10-15)²/15

χ² = 5²/15 + (-3)²/15 + 3²/15 + (-5)²/15

χ² = 4.533

The critical value :

df = n - 1 ; 4 - 1 = 3

χ²critical (0.05, 3) = 7.815

Decison region :

|χ²| < χ²critical ; Fail to reject the null

For this analysis ;

|χ²| < χ²critical ; Fail to reject the Null

Hence, there is insufficient evidence to suggest that preference exists among the four colors