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Theory-Based Inference
(adapted from Examples 1.3 and 1.4)
Example 1.4: Halloween Treats
Recall that stemming from concern over the nation’s obesity epidemic, researchers investigated
whether children might be as tempted by toys as by candy for Halloween treats. Test
households in five Connecticut neighborhoods offered children two plates: one with lollipops or
fruit candy and one containing small, inexpensive Halloween toys, like plastic bugs that glow in
the dark. The researchers observed the selections of 283 trick-or-treaters between the ages of 3
and 14 (Schwartz, Chen, and Brownell, 2003). ï€ To investigate whether children show a preference for either the candy or the toys, we test the
following hypotheses.
Null hypothesis: The probability a trick-or-treater would choose candy is 0.5.
Alternative hypothesis: The probability a trick-or-treater would choose candy is not 0.5.
Note that our null model assumes that the probability of choosing candy (π) is the same for all
children. In symbols, these hypotheses translate to
H0: 𝜋 = 0.5
Ha: 𝜋 ≠0.5.
The researchers collect the reactions of 283 children for the study. With a sample size of 283,
under our null hypothesis, we simulated the null distribution (using 10,000 simulated samples)
shown in Figure 1.1.
Figure 1.1: A null distribution representing 10,000 simulated samples of 283 children where the
probability that an individual child would choose candy is 0.5
1. With regard to the above null distribution:
a. What is the numeric value of the center of this null distribution? Does that make
sense?
b. What is the SD of this null distribution?
June 27, 2014
MAA PREP workshop
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