symmetric distribution, the mean is approximately located at this center. Therefore, because
the mean of this distribution is approximately equal to the population mean of 428 grams, we
have evidence that we are using an unbiased estimator.
b. There are only two simulated bags out of the 300 simulated samples that have a mean weight
of more than 446.2 grams. This is a simulated probability of only 0.0067. Given how small a
probability, it seems unlikely that the farmers’ market is correct in its claim about the
population of bags of grapefruit.- Cortisol
a. Put all 100 volunteers’ names on equally sized pieces of paper into a hat and mix thoroughly.
Then draw the names one at a time out of the hat. The first 50 names drawn are the volunteers
who will receive the black tea capsules. The remaining 50 names are the volunteers who will
receive coffee capsules.
b. Using capsules keeps the volunteers blind to which treatment they are receiving so that any
effect can be attributed to the treatment (tea or coffee concentrate) rather than perhaps the
placebo effect.
c. It is not reasonable to generalize the results of this study to all adults. The sample was a
voluntary one, not a random one.
Summer enrichment program
a. There appears to be an association between course option choices and age as the distributions
are so different. Specifically, the proportion of sophomores who chose music is higher than
that of juniors and much higher than that of the freshmen. The proportion of juniors who chose
academics is about the same as that of sophomores, but much lower than that of the freshmen.b. H (^) o : Choice of enrichment program is the same for the populations of freshmen, sophomores,
and juniors.
H (^) o : Choice of enrichment program is not the same for all three populations.
c. Since the P -value is so low, lower than any reasonable value of alpha, the district
administrators should reject the null hypothesis. It appears that the choice of enrichment
program is not the same for all three populations of students.
Affordable housing
a. The graduate student should not use a t -test for this hypothesis because the sample is so small
and contains one outlier of 70.4 percent.
b. The table should be filled in as follows:c. Once the variable has been changed to a categorical variable (above/below), the outlier
ceases to be an issue.
d. This is now a binomial probability with n = 8 and P (below the median) = 0.50. The
approximate probability that 1 or fewer clients would have a housing expense percentage of