Refer to the previous exercise about investigating whether infants tend to look at surprising events or behavior for longer times, on average, compared to uninteresting ones?

a. Define, in words, the appropriate parameter(s) of interest in the context of the study. Also, state the appropriate symbol(s) to denote the parameter(s).
b. State, using the symbol(s) described in part (a), the appropriate null and alternative hypotheses in the context of the study.
c. State the validity conditions that have to be met to be able to perform a theory-based test to test the hypotheses stated in part (b). Are these conditions met? How are you deciding?
d. Regardless of your answer to part (c), perform a theory-based test to test the hypotheses stated in part (b). Be sure to report a test statistic value and a p-value in your answer.
e. Interpret your p-value in the context of the study.

f. Find and interpret a 95% confidence interval for the parameter of interest in the context of the study.
g. Give a full conclusion with regards to statistical significance, estimation (confidence), causation, and generalization.

Data from previous exercise

Researchers Hamlin et al. (Nature, 2007) conducted a study with 16 infants that involved an assessment of infants€™ expectations of a climber toy€™s attitude towards a €œhelper€ (a toy figure that helped the climber climb a hill) and a €œhinderer€ toy (a figure that had hindered the climber€™s progress up a hill) and whether infants tend to watch the climber€™s confrontation with the hinderer for a longer time than that with the helper. Each of the sixteen 10-month-olds was shown a new display where the climber would alternately approach the helper and the hinderer, of which the latter was considered to be a surprising event, because such an action was perceived as €œviolation of the expectation paradigm.€ The lengths of time that each infant spent watching the climber approach the helper and the hinderer was recorded, and it was noted that in the study the infants looked longer at the approach of the climber towards the hinderer than the helper. (Wonder if the infants were expecting the climber to punch the hinderer, and that held their interest longer!) Given below are some summary statistics for the difference (hinderer ˆ’ helper) in looking times (seconds). Note that the distribution of differences is fairly symmetric.

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Mean SD Difference Time Hinderer - TimeHelper 1.752 sec 1.140 sec 16