Cake or Broccoli? When children are just learning to speak, they are likely to mimic what they just heard. For example, when asked "Do you want cake or broccoli?", a child might answer broccoli just because it was the last option presented. (This is called "recency bias" in psychology.¹) In a study² examining this effect, two-year-old children were asked to choose between two options. In Experiment 1, each binary-choice question included pictures of the two options, and children answered by pointing at a picture. In Experiment 2, the question was only given verbally, and children answered verbally. In each case, test to see if the second option is more likely to be picked than the first, which means the proportion of times the second option is chosen is greater than 0.5. Give all details of the test in each case: hypotheses, sample statistic, p-value, and conclusion in context.

¹The recency bias seen in two-year-olds appears to disappear by the age of 4. As we saw in Exercise 1.63, adults are more likely to show the primacy effect, in which the first choice given is more likely to be the one selected.

²Sumner E, et al., "Cake or broccoli? Recency biases children's verbal responses," PLoS ONE, 14(6), June 12, 2019.

(a) In Experiment 1 with pictures, the toddlers picked the second choice 248 times out of 480 trials.

State the null and alternative hypotheses.

(b) Give notation of the sample statistic.

c) Give value of the sample statistic accurate to three decimal places.

d) Use a randomization distribution to find the p-value. Give your answer accurate to three decimal places.

e) State the conclusion in context.

• Reject H₀. We have evidence that two-year-olds prefer the second option when presented with pictures.
• Reject H₀. There is not enough evidence to say that two-year-olds have a preference when presented with pictures.
• Do not reject H₀. We have evidence that two-year-olds prefer the second option when presented with pictures.
• Do not reject H₀. There is not enough evidence to say that two-year-olds have a preference when presented with pictures.

f) (b) In Experiment 2 with only words, the toddlers picked the second choice 409 times out of 480 trials.

State the null and alternative hypotheses.

g) Give notation of the sample statistic.

h) Give value of the sample statistic accurate to three decimal places.

i) Use a randomization distribution to find the p-value. Give your answer accurate to three decimal places.

j) State the conclusion in context.

• Reject H₀. We have evidence that two-year-olds prefer the second option when presented with options verbally.
• Reject H₀. There is not enough evidence to say that two-year-olds have a preference when presented with options verbally.
• Do not reject H₀. We have evidence that two-year-olds prefer the second option when presented with options verbally.
• Do not reject H₀. There is not enough evidence to say that two-year-olds have a preference when presented with options verbally.