As Children Grow They Develop What Is Known as "Representational

Essay

As children grow they develop what is known as "representational insight," a connection between an object and a symbol for that object. A random sample of youngsters 24-months old were shown a video of someone putting a toy under 1 of 4 randomly placed boxes in a room familiar to the child. They were then taken to the room, and asked to "find the toy." The investigators reasoned that a child with representational insight should pick the correct box on the first try. If the children were to overturn the boxes randomly, they would find the toy on the first turn 25% of the time. Thirty children out of 57 subjects found the toy by turning over the correct box on the first try.
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Does this sample provide sufficient evidence that the proportion of 24-month old children who choose the correct box on the first try is greater than 0.25? Use a significance level of α = 0.05 to test the appropriate hypothesis.