Two-sided Alternatives

We suspect that some of you answered "too small" and some of you answered "too large" to the previous question. Oftentimes, we may want to gather evidence against a particular value for the parameter, but would be curious to know whether it was either too large or too small (e.g., a bolt is not going to be very effective in holding a door together if it's too large or if it's too small). When researchers don't have a prior conjecture in advance as to how a null hypothesis is false (and before we peek at the data!), they can specify a two-sided alternative. If we let pi represent the probability of a kissing couple turning right, we could state the hypotheses as:

Thought Questions (Think about briefly, discuss with partner, move on):

How does this change to the alternative hypothesis impact how we will calculate the p-value? What values will we consider evidence against the null hypothesis?

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