Question

3. In a study examining colour preferences in infants, 32 babies were offered a choice between a red rattle and an otherwise identical green rattle. (a) What would a reasonable a priori claim concerning rattle choice be? (Hint: what would p be expected to be, on average, if babies preferred no one colour over the other?) In fact, 22 of the 32 selected the red rattle What proportion of babies, p, chose the red rattle? (c) What proportion, q, chose the green rattle? (d,e) Check that approximating the data using the Normal distribution is valid and record your results. Test a reasonable claim about colour preference among the infants in this study. (State (f) claim, (g) counter-claim, (h) null and (i) alternative hypotheses, (i) test statistic used, (k) its numerical value, (I) its P equivalent and (m) your conclusion in language that a baby's parents would understand). (Gravetter& Walnau, 1996, 4th ed, p 596.) 13 7 . (b)

Answer 1

a)
p = 1/2
b)
p^ = 22/32

c)
q^ = 1 - 22/32 = 10/32

d)
np = 22 > 5
nq = 10 > 5
hence normal approximation is valid
e)
Z = (p^ -p)/sqrt(pq/n))
= (22/32 - 0.5)/sqrt(0.5*0.5/32))
= 2.12132
f)
claim : proportion of choosing red rattle is 1/2
g)
proportion of choosing red rattle is not 1/2

h)
Ho: p= 1/2
Ha: p not equal 1/2

i)
p-value = 2 P(Z >2.12132)
= 2*0.0169
=0.0338

m)

p-value < 0.05

we reject the null hypothesis , we conclude that p is not equal to 1/2