Children Develop "Representational Insight," a Connection Between an Object and a Symbol

Essay

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 $\alpha = .05$ to test the appropriate hypotheses.