Question

A recent study suggested that 81% of senior citizens take at least one prescription medication. Amelia is a nurse at a large hospital who would like to know whether the percentage is the same for senior citizen patients who go to her hospital. She randomly selects 59 senior citizens patients who were treated at the hospital and finds that 49 of them take at least one prescription medication. What are the null and alternative hypotheses for this hypothesis test?

Answer 1

Null hypothesis: $p = 0.81$

Alternative hypothesis: $p \ne 0.81$

The null is based on a recent study that 81% of the population (in this case senior citizens) takes at least one medication. The alternative hypothesis is basically the flip of the claim made in the null.

If Amelia wanted to know if the percentage was less than 81%, then the alternative would be p < 0.81

If Amelia wanted to know if the percentage was larger than 81%, then the alternative would be p > 0.81

However, she wants to know if the percentage is 81%.