Other research examining the effects of preschool-childcare has found that child

Question

Other research examining the effects of preschool-childcare has found that children who spent time in day care, especially high-quality day care, perform better on math and language tests than children who stay home with their mothers (Bromberg Wessel, Lamb, & Hwang 1997), Typical results, for example, show that a sample of n = 25 children who attended day care before starting school had an average score of M - 87 with SS = 1536 on a standardized math test for which the population mean is mu = 81. Is this sample sufficient to conclude that the children with a history of preschool day care are significantly different from the general population? Use a two-tailed test with alpha = .01. Compute Cohen's d to measure the size of the preschool effect. Write a sentence showing how the outcome of the hypothesis test and the measure of effect size would appear in a research report.

Explanation / Answer

Step 1: Hypotheses and H0: = 81 H1: 81 = 0.01

Step 2: Critical region = 0.01 Two-tailed df = n – 1 = 25 – 1 = 24 tcritical = 2.797

Step 3: Calculate tobserverd

s 2 = SS / (n – 1) = 1536 / (25 – 1) = 64

s = s2 = 64 = 8

sM = (s2 / n) = (64 / 25) = 1.6

t = (M – ) / sM

= (87 – 81) / 1.6 = 3.75

Step 4: Decide The observed t (3.75) is in one of the tails cut off by the critical t (2.797), therefore we reject H0. It is likely that attending preschool changes math performance.

b.Compute Cohen’s d to measure the size of the preschool effect. estimated

d = (M – ) / s = (87 – 81) / 8 = 0.75

c,Infants who attended preschool scored an average of M = 87 on a standardized math test with SD = 8.00. Statistical analysis indicates that the score is significantly different than the population mean of 80,

t(24) = 3.75, p .05, Cohen’s d = 0.75.

Hope this will help you. God bless you. thanks:)

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