On a late-night infomercial, a new dealer of pre-packaged diet meals and non-FDA approved diet supplements promises viewers that they will lose an average of at least 20 pounds in just six weeks (individual results may vary). A consumer watchdog who watches too much late-night TV wants to dispute this claim. She digs up a random sample of 16 wannabe weight losers who have used these products for six weeks. The number of pounds lost by each of these people is as follows: 18 19 22 17 15 23 18 19 19 17 20 18 19 22 17 18 Upon consulting a nutritional expert, she also receives assurance that it is reasonable to assume σ = 2.4 for the population of consumers of this supplement.

State carefully the conclusion you would reach at the 1% level of significance?

On a late-night infomercial, a new dealer of pre-packaged diet meals and
non-FDA approved diet supplements promises viewers that they will lose an
average of at least 20 pounds in just six weeks (individual results may
vary). A consumer watchdog who watches too much late-night TV wants to
dispute this claim. She digs up a random sample of 16 wannabe weight losers
who have used these products for six weeks. The number of pounds lost by
each of these people is as follows:
18 19 22 17 15 23 18 19 19 17 20 18 19 22 17 18
Upon consulting a nutritional expert, she also receives assurance that it is
reasonable to assume σ = 2.4 for the population of consumers of this
supplement.
a) Find the sample mean.
b) Do these data give good evidence that the true mean weight loss is less
than 20 pounds? Carry out the appropriate test: state null and alternative
hypotheses, identify the test statistic, determine the P-value.
c) State carefully the conclusion you would reach at the 1% level of
significance.
d) State carefully the conclusion you would reach at the 5% level of
significance.