A researcher has developed a new diet and she hypothesizes that people will
lose weight with her regimen. She tests this hypothesis against the null hypothesis
that people's weights will remain the same. She tries the diet on 3 people, and they
experience weight losses of 3, 4, and 3.5 pounds, respectively.
(a) Assuming that the weight loss is normally distributed, give a range of the
pvalue
that the researcher should report.
(b) Suppose that there is a malfunction of the scale used to weigh the participants
and instead of the results obtained above, the weight losses are shown to be 3,
4, and 15 pounds, respectively. Working from these data, give a range of the
p-value that the researcher should report.
(c) What is a possible explanation for the paradoxical results of (a) and (b)?