# Thread: Hypothesis testing.

1. ## Hypothesis testing.

A common medicine for relieving serious pain is believed to be only 80% effective. A new
medicine is used to a random sample of 100 adults who were suffering from serious pain and it
shows that 85 received relief. Is this sufficient evidence to conclude that the new medicine is
superior to the one commonly prescribed? Use a 0.05 level of significance.

2. where are you stuck?

find the probability that 85 or more people would be relieved if it was only 80% effective, and see if this is more or less than 0.05.

3. $H_0=.8" alt="H_0=.8" /> vs. $H_a>.8" alt="H_a>.8" />

Test stat is ${\hat p-p_0\over \sqrt{p_0q_0/n}}$

which is approximately normal, so use $(1.645,\infty)$ as your rejection region.