- (A) Bias is defined as any process that systematically over- or underestimates. A process that creates
estimates that are, on average, too high or too low is, by definition, biased.
- (B) A Type I error means the null hypothesis is true, but you reject it. That means pizza places, on
average, do not make over $9,000 per month, but you believe they do. You might open a business and
do poorly.
- (A) We need to find the z -score that corresponds to a lower-tail area/probability of 0.2800. Using
Table A (see Appendix), that z -score is −0.58. −0.58 · 2.1 ounces = −1.22 ounces, so this onion is
1.22 ounces below the mean.
- (D) Because there is an association between exercise and cholesterol, we need to block on level of
exercise.
- (E) If we are to use the data that were returned, then we have to find a way to overcome nonresponse
by getting survey results from those who did not return the survey.
- (D) A factor is an explanatory variable. Replication means that, within an experiment, each treatment
is applied to more than one experimental unit. Treatments are combinations of levels from different
factors. The variable controlled by researchers is the explanatory variable, not the response variable.
D is the only correct option.
- (D) The key phrase in this question is “most representative sample of its customers.” Choice (D)
ensures that the sample selects customers from each state and that selection is proportional to the
number of customers from each state. For example, if 25% of the customers are from California, then
25% of the sample will be from California.
- (C) In order to use a normal approximation to a binomial model such as this, we should see if np and
n (1 – p ) are both at least 10. (Note, some authors will check to see if both are at least 5 and others
will check to see if both are at least 15.)
- (B) We need to calculate P (Serenity in first box, Blackstar in second box) as well as P (Blackstar in
first box, Serenity in second box) and then add them. This would be (0.12)(0.18) + (0.18)(0.12) =
0.0432.
- (B) Using the expected value formula for a probability function we get (0.05)(0.45) + (0.10)(0.25) +
(0.15)(0.15) + (0.25)(0.10) + (0.50)(0.05) = 0.12, or 12%.
- (C) The probability of selecting a player above the third quartile is 0.25 because we are sampling
with replacement, this situation meets the conditions of a binomial variable with n = 5 and
probability of success = 0.25. Therefore, P (x ≥ 3) = P (3) + P (4) + P (5). Using the formula
we get, P (3) + P (4) + P (5) = 0.1035.
- (C) The mean of the total weight is the same as the sum of the individual means, or 62 grams + 456
grams = 518 grams. We are told that the shipping is secured in an independent part of the factory, so
therefore the variance of the total weight is given by (1.0 grams)^2 + (6 grams)^2 . We find the standard
deviation of the total weight by taking the square root of that variance, or = 6.1 grams.
- (A) Recall that two events A and B are independent if P (A|B = P (A). The proportion of juniors in
the group who vote for pizza is 48/144 = 0.33333. The proportion of all students who vote for pizza
is 195/585 = 0.3333. Since these are the same value, Student is a junior and Student choses pizza
are independent.
