Children develop \"representational insight,\" a connection between an object an

Question

Children develop "representational insight," a connection between an object and a symbol for that object. A random sample of 2-year olds were shown a video of someone putting a toy under 1 of 4 randomly placed boxes in a room familiar to the child. Then they were taken to the room, and asked to "find the toy."   The investigators reasoned that a child with representational insight would pick the correct box on the first try. If not, they would find the toy on the first try only 25% of the time.   Thirty out of 57 children found the toy by turning over the correct box on the first try.

    Do these results provide convincing evidence that the proportion of 2-year old children who choose the correct box on the first try is greater than 0.25? Use a significance level of to test the appropriate hypothesis.

Explanation / Answer

Solution:

Expected proportion = E = 25% = 0.25
Observed proportion = O = 30/57 = 0.53
Ho: p </= 0.25
Ha: p > 0.25 (One tailed test)
Standard error of proportion = S.Ep = sqrt (p*(1-p)/n)
= sqrt (0.25*0.75/57)
= 0.0574
Calculated z-value = Test criterion = (O-E) / S.Ep
= (0.53 - 0.25) / 0.0574
= + 4.88
Critical value of z at alpha = 0.05 is 1.645 (for one tailed test)
Since the calculated z value is > the critical value of z, the Ho will be rejected.
Ha will be accepted.

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