A researcher wishes to determine if the use of an herbal extract improves memory. Subjects will take the herbal extract regularly during a 10‑week period, and then each subject will have a standard memory test. Suppose the scores on this test, for all potential subjects taking the herbal extract, follow a Normal distribution, with mean and standard deviation =6
. Suppose also that, in the general population of all people, scores on the memory test follow a Normal distribution, with mean 50 and standard deviation =4
. The researcher, therefore, decides to test the hypotheses 0:=50
, :>50
. To do so, he has 100 subjects follow the 10‑week protocol. The mean score for these students is ¯=55.2
, and the
‑value is less than 0.0001.
Which of these choices is an appropriate conclusion?

None of the answer options are correct.

The researcher has strong evidence that the use of this herbal extract improves memory and, because the
‑value is so small, the difference must be substantial.

The researcher has strong evidence that people who use this herbal extract, on average, have higher memory test scores than those who don’t use this extract. However, the difference may or may not be important.

The researcher has conclusively proved that the use of this herbal extract improves memory.