# Worksheet 18: Multiple hypotheses

Your name:

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## Practice quiz \#3

A candy company promises that at least 30% of their chocolate eggs contain a figurine of the fictional character Elsa from Frozen; the rest contain other toys. Suppose you buy 40 chocolate eggs, and only 9 of them contain an Elsa figurine.

You will investigate whether the low number of Elsa figurines is statistically significant.

1. What are the null and alternative hypotheses? Describe them both in English and in mathematical symbols.



2. Describe how you would do a simulation to compute a p-value. If the null was true, what would be the "probability of success"? What would be the "number of trials"? What value would you compare the simulated data to?



3. The p-value for the observed results (an Elsa figurine in 9 of the 40 chocolate eggs) is 0.04. What do you conclude about the null hypothesis?




## Bonferroni example

4. In the xkcd comic, what should be the Bonferroni correction?



## Dream again

5. Last lecture, we saw that Dream was unlikely to get so many Ender pearls by luck. But, do we need to do a multiple hypothesis correction?



6. How could we do a Bonferroni correction for Dream? What is $m$ the number of hypotheses?



7. Perform a Fermi estimate for $m$.