Each question is followed by five suggested
answers labeled "a" through "e". Circle the ONE that
best answers the question. Make sure your choice is clear.
1. The results of an experiment are said to be
statistically significant if... ?
a. They are important to statisticians, regardless of their importance to the investigators.
b. Both investigators and statisticians agree the results are meaningful and important.
c. If the results are important to the investigators, regardless of their importance to the statisticians.
d. The observed effect is too large to attribute plausibly to chance.
e. They support the findings of previous, similar studies.
I. The standard deviation of the sample mean is .
II. As n increases then approaches .
III. The distribution of the population is approximately normal.
a) I only.
b) II only
c) I and II.
d) II and III.
e) I, II, and III.
3. When performing a test of significance for a
null hypothesis, Ho, against an alternative hypothesis, Ha, Type II error
a) the probability that Ha is true.
b) the probability that Ha is false.
c) the probability of rejecting Ho if Ha is true.
d) the probability of not rejecting Ho if Ha is true.
e) the probability of not rejecting Ho if Ho is true.
4. A large university estimates the mean age for
female students on its campus by testing a SRS of 200 female students and
constructing a 95% confidence interval based on their ages. The resulting
confidence interval is: (18.1, 22.3)
I. The mean age for the population of all females at the university is in (18.1, 22.3)
II. In the long run, 95% of similarly constructed confidence intervals will contain the mean age for the population of all females at the university.
III. By increasing the confidence level in this computation, the confidence interval will become narrower.
a) II only.
b) I and II.
c) II and III
d) I and III.
e) I, II, and III.
5. Each of the five pictures below has the same boxplot. Which one of the following histograms was generated from the same data as the boxplot?
6. In addition to control by comparing several
treatments, the TWO other basic principles which distinguish experiments
from observational studies include:
I) randomization, i.e. assigning researchers by chance
II) randomization i.e. assigning subjects by chance
III) replication, i.e. doing a study more than once
IV) replication, i.e. doing a study with many subjects
V) blocking to remove bias
a) I and III
b) I and IV
c) II and III
d) II and IV
e) IV and V
7. The following two-way table categorizes suicides committed in 1983 by the sex of the victim and the method used.
From this table, what would be the best conclusion
a. Simpson's Paradox was demonstrated by the data.
b. There was no relation between the sex of the victim and the method of suicide used.
c. Females were responsible for a higher percentage of the suicides committed by using poison than males.
d. Males accounted for roughly 77% of all suicides, regardless of method.
e. Firearms were used in roughly 90% of all suicides,
regardless of sex.
Directions: Show some supporting work on each question.
|8. The histogram to the right describes the number of children in a study of Clayton State College families. Determine the median number of children per family without entering specific data items into your calculator.|
9. State the Empirical Rule and find a more exact value for any one of its values (accurate to 2 decimal places).
10. The SAT and ACT are two tests which students often take when applying to college. Assume the distribution of scores on the SAT is N(500,100) and the ACT is N(18,6). Corkey scored a 660 on the SAT. What score would Bob need on the ACT to have done "as well" as Corkey?
11. We studied x-bar control charts which used
sample means. BPS states that there are also p-hat control charts which
are centered on the mean of p-hat and have control limits at three standard
deviations of p-hat . A manufacturer is working with a process that normally
has failure rate of 10%, i.e. the mean of p-hat is 0.1 in the long run.
They sample n boards for each shift and record the failure rate on the p-hat
control chart. What must n be to keep the upper control limit at 30%, i.e.
12. Pain-Be-Gone, a new treatment for muscular pain, is successful in 45% of the cases. What is the exact probability that 10 or 11 out of 15 randomly selected, unrelated patients will be cured with Pain-Be-Gone?
13. Modeling: In making financial decisions
about retirement it is important to make an educated guess about how long
you might live after you retire. Almost all faculty at BB&N have some
of their retirement money in a company called TIAA/CREF. Last month the
TIAA/CREF Newsletter published the table below. It displays data for the
number of years you can expect to live if you are presently at a certain
age. Note the data set below is incomplete so that you are NOT tempted
to enter it into you calculator.
a. The slope of the Least Squares Regression (LSR) line for the given data is approximately 0.75 . Interpret this number in terms of the actual problem.
b. If r = 0.97, write the most accurate sentence
possible describing how well the LSR MODEL FITS THE DATA.
c. Residuals plots for a LSR model and a Quadratic
Model are shown above to the right. The key helps you distinguish between
the two. Note also that the coordinates for one residual are displayed.
Determine which one of the two models is better at describing the data.
d. Without using the equation of the LSR line determine what this model predicts your life expectancy to be if your present age is 100 years. Show your work.
14. Tests of Significance:
a) Demonstrate that you understand all the steps of a fully annotated Test of Significance in analyzing the following question:
The average income of restaurant waiters and waitresses in a large city is $231 per week with a standard deviation of $15 and forms a normal distribution. Waiters and waitresses from the north part of town believe they are not being paid the same amount of money as the rest of the town and hire an investigator. The investigator collects income data from a simple random sample of 75 restaurant workers in the northern part of town and finds the sample mean to be $227 per week and decides to test this sample at a 0.03 level of significance.
b) Calculate by hand, i.e.. without using
the STAT TEST menu of your calculator, an appropriate confidence interval
associated with the question in part a) and explain its relationship to
the question in part a). Show your work.
|You are required to do one or the other of the following two problems. Your choice.|
b. Show an annotated diagram of graphs of distributions
which demonstrates clearly that you understand the term Power of a Test
for the previous problem (#14).