As children grow they develop what is known as \"representational insight,\" a c

Question

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. 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 a .05 to test the appropriate hypothesis. (Define the parameter of interest state the null and the alternative hypotheses; check the assumptions of the test; clearly mention the test statistic and calculate its value; calculate the p-value of the test; make your conclusion in terms of the context.)

Explanation / Answer

Representational Insight

In this hypothesis test, parameter of interest is the proporterion onf 24 months old youngsters with representational insight.

Below are the null and alternate hypothesis
H0: p <= 0.25
H1: p > 0.25

pcap = 30/57 = 0.5263
test statistics, z = (0.5263 - 0.25)/ sqrt(0.25*0.75/57) = 4.8174

p-value = 0
As p-value is less than the significance level of 0.05, we reject the null hypothesis.
This means there is significant evidence that proportion of 24 months old youngseters with representational insight.

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