Research examining the effects of preschool childcare has shown that children wh

Question

Research examining the effects of preschool childcare has shown that children who spend time in day care, especially high-quality day care, perform better on math and language tests than children who do not attend day care. [Broberg, A. G., Wessels, H Lamb, M. E. & Hwang, C. P. (1997). Effects of day care on the development of cognitive abilities in 8-year-olds: A longitudinal study. Development Psychology, 33, 62-69. 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 1,536 on a standardized math test for which the population mean is H 81 Is this sample sufficient to conclude that the children with a history of preschool day care are significantly different in terms of cognitive ski from the general population? U a two-tailed test with o .01. (U three decimal places for se se the critical value, two for the t statistic.) t Distribution Degrees of Freedom 21 1.0 2.0 3.0 t-critical Conc O Reject the null hypothesis; children with a history of day care have significantly different cognitive skills. O Fail to reject the null hypothesis; children with a history of day care do not have significantly greater cognitive O Fail to reject the null hypothesis; children with a history of day care do not have significantly different cognitive skills. O Reject the null hypothesis; children with a history of day care have significantly greater cognitive skills. Compute Cohen's d to measure the size of the preschool effect. Estimated Cohen's d

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 t observerd

s2 = SS / (n – 1) = 1536 / (25 – 1) = 64

s = s2 = 64 = 8

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

t = (M – ) / SM

t = (87 – 81) / 1.6

t = 3.75

critical t (2.797),

t = 3.75

Conclusion:

Reject the null hypothesis' children with history of day care have significantly different cognitive skills H0.

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

estimated d = (M – ) / s = (87 – 81) / 8 = 0.75

The result show that the standardized math test scores statistically significantly different for children with a history of day care than for other children who do not attend day care

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