Data 4.3 on page 265 introduces a situation in which a restaurant chain is
measuring the levels of arsenic in chicken from its suppliers. The question is
whether there is evidence that the mean level of arsenic is greater than \(80
\mathrm{ppb},\) so we are testing \(H_{0}: \mu=80\) vs \(H_{a}:\) \(\mu>80,\) where
\(\mu\) represents the average level of arsenic in all chicken from a certain
supplier. It takes money and time to test for arsenic, so samples are often
small. Suppose \(n=6\) chickens from one supplier are tested, and the levels of
arsenic (in ppb) are:
\(\begin{array}{llllll}68, & 75, & 81, & 93, & 95, & 134\end{array}\) (a) What
is the sample mean for the data?
(b) Translate the original sample data by the appropriate amount to create a
new dataset in which the null hypothesis is true. How do the sample size and
standard deviation of this new dataset compare to the sample size and standard
deviation of the original dataset?
(c) Write the six new data values from part (b) on six cards. Sample from
these cards with replacement to generate one randomization sample. (Select a
card at random, record the value, put it back, select another at random, until
you have a sample of size \(6,\) to match the original sample size.) List the
values in the sample and give the sample mean.
(d) Generate 9 more simulated samples, for a total of 10 samples for a
randomization distribution. Give the sample mean in each case and create a
small dotplot. Use an arrow to locate the original sample mean on your
dotplot.
