January 1998

AP Statistics Examination

Mr. Coons

  • Check now that you have 8 pages.
  • Work and answers should be done on these pages. If necessary, extra sheets can be ATTACHED.
  • Note that you have a choice of one of two problems when doing the last problem.

Name:



A. Multiple Choice

Directions: 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.



2. Given a SRS of size n from a population of with mean
and standard deviation , which of the following statements must be true?

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 is:

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.


Method Male Female Row totals
Firearms 13,959 2,641 16,600
Poison 3,148 2,469 5,617
Hanging 3,222 709 3,931
Other 1,457 690 2,147
Total 21,786 6,509 28,295

From this table, what would be the best conclusion about 1983?

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.



B. Smaller Questions

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. 0.3?


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?



C. Problems which contain some Open-Ended Responses

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.

 Present
Age (years)
 30

35

40

45 

50

55

60

65

70

75

80

85

90

95
 100

 Life Expectancy (years)
 55.1  50.3  45.4

40.6

 36.0
 

31.4

27.0

22.8

18.7

15.0

11.6

8.8

6.5

4.8

         

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. Explain why.

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.



D. Create Your Own

 You are required to do one or the other of the following two problems. Your choice.


15. a. Did you read the instructions above? Demonstrate your understanding of "both parts" of the Law of Averages by explaining it to a new AP Statistics student. Your work should include the description of a specific simple experiment, the numerical results (which you make up so that they are realistic), and an explanation of how these results demonstrate the Law.

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).


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