91Ó°ÊÓ

Yale University graduate student J. Kiley Hamlin conducted an experiment in which 16 ten-month-old babies were asked to watch a climber character attempt to ascend a hill. On two occasions, the baby witnesses the character fail to make the climb. On the third attempt, the baby witnesses either a helper toy push the character up the hill or a hinderer toy prevent the character from making the ascent. The helper and hinderer toys were shown to each baby in a random fashion for a fixed amount of time. The baby was then placed in front of each toy and allowed to choose which toy he or she wished to play with. In 14 of the 16 cases, the baby chose the helper toy. Source: J. Kiley Hamlin et al., "Social Evaluation by Preverbal Infants." Nature, Nov. 2007. (a) Why is it important to randomly expose the baby to the helper or hinderer toy first? (b) What would be the appropriate null and alternative hypotheses if the researcher is attempting to show that babies prefer helpers over hinderers? (c) Use the binomial probability formula to determine the \(P\) -value for this test. (d) In testing 12 six-month-old babies, all 12 preferred the helper toy. The \(P\) -value was reported as \(0.0002 .\) Interpret this result.

Suppose we are testing the hypothesis \(H_{0}: p=0.3\) versus \(H_{1}: p>0.3\) and we find the \(P\) -value to be \(0.23 .\) Explain what this means. Would you reject the null hypothesis? Why?

If the consequences of making a Type I error are severe, would you choose the level of significance, \(\alpha,\) to equal \(0.01,0.05,\) or \(0.10 ?\) Why?

The headline reporting the results of a poll conducted by the Gallup organization stated "Majority of Americans at Personal Best in the Morning." The results indicated that a survey of 1100 Americans resulted in \(55 \%\) stating they were at their personal best in the morning. The poll's results were reported with a margin of error of \(3 \% .\) Explain why the Gallup organization's headline is accurate.