Computational problems – practice for Exam 3
1. The mean number of standard drinks of an alcoholic
beverage per week in the population of US adult drinkers is
4.8.
a. What additional information is needed in order to be able to
use the z-tables to determine the probability of obtaining a
sample with a mean that differs from the population mean by
0.4 drinks or more?
b. You’ve obtained a random sample of 25 US adult drinkers
and have computed the sample mean to be 5.2 drinks per
week. If the population standard deviation is 3.0, what is the
probability of obtaining a sample with a mean that differs from
the population mean by this much or more? You may now
assume that number of drinks per week among the adult
drinking population is normally distributed.
c. Draw a sketch of the population distribution for this
problem.
d. Draw a sketch of the sampling distribution of the mean for
this problem. Shade the area(s) corresponding to the
probability that you determined in part b.
(continued)
2. You are interested in how the alcoholic beverage drinking
behavior among college seniors compares to the national
average among drinking adults. You decide to test a nondirectional null hypothesis that their drinking does not differ
on average from the national adult population.
a. State your statistical null and alternative hypotheses (use
symbols for the population parameters you are interested in):
b. You randomly sample 36 college seniors and compute the
mean number of drinks per week in this sample to be 6.0.
Using the pertinent information from question 1 above, what is
the probability of obtaining a sample mean that differs this
much or more from the population mean if the null hypothesis
is true?
c. Does the mean of your sample fall into the region of
rejection?
d. Can you reject Ho?
e. What can you conclude from your study?
3. Assume now that you did NOT know the standard deviation
of the population of US adult drinkers.
a. Are you still able to test the null hypothesis from question
2? If yes, what additional information will you need? If no,
explain why not.
b. Assume the information you obtained from your sample of
36 seniors included: mean = 6.0; S = 3.2; s = 3.25; Q = 1.6.
c. Does the mean of your sample fall into the region of
rejection?
d. What can you conclude from your study?