|
AP Statistics / Mr. Hansen |
Name: _________________________________ |
Test #6 SAMPLE (3/9/1999)
General Instructions: INDICATE ALL YOUR ANSWERS TO QUESTIONS ON THE SEPARATE ANSWER SHEET ENCLOSED. No credit will be given for anything written on this test form, but you may use the booklet for notes or scratchwork. After you have decided which of the suggested answers is best, COMPLETELY fill in the corresponding oval on the answer sheet. Give only one answer to each question. If you change an answer, be sure that the previous mark is erased completely.
Example:
What is the arithmetic mean of the numbers 1,
3, and 6 ?
(A) 1
(B) 7/3
(C) 3
(D) 10/3
(E) 7/2
Answer:
|
A |
B |
C |
D |
E |
|
O |
O |
O |
· |
O |
Many students wonder whether or not to guess the answers to questions about which they are not certain. In this test, as a correction for haphazard guessing, one-fourth of the number of questions you answer incorrectly will be subtracted from the number of questions you answer correctly. It is improbable, therefore, that mere guessing will improve your score significantly; it may even lower your score, and it does take time. If, however, you are not sure of the best answer but have some knowledge of the question and are able to eliminate one or more of the answer choices as wrong, your chance of answering correctly is improved, and it may be to your advantage to answer such a question.
Use your time effectively, working as rapidly as you can without losing accuracy. Do not spend too much time on questions that are too difficult. Go on to other questions and come back to the difficult ones later if you have time.
1. When two types of detergent are spritzed onto a cloth, small discolorations may appear because of imperfections in manufacturing. To compare the mean number of discolorations produced by the detergents, a measured quantity of one detergent is applied to half of each of 8 swatches of cloth, and the same amount of the other detergent is applied to the other half of each swatch. The detergent that goes on the right half of the swatch is decided by a coin flip. The discolorations that appear on each half are then counted. The data are given below.
|
Swatch |
Detergent 1 |
Detergent 2 |
|
1 |
20 |
18 |
|
2 |
18 |
14 |
|
3 |
7 |
5 |
|
4 |
10 |
6 |
|
5 |
5 |
9 |
|
6 |
14 |
13 |
|
7 |
14 |
12 |
|
8 |
8 |
12 |
What is the number of degrees of freedom associated with the appropriate t-test for testing to see if there is a difference between the mean number of discolorations per swatch produced by the two detergents?
(A) 7
(B) 8
(C) 11
(D) 14
(E) 16
2. Which of these is a criterion for choosing a z-test rather than a t-test when making an inference about the mean of a population?
(A) The standard deviation of the population is unknown.
(B) The mean of the population is unknown.
(C) The standard deviation of the population is known.
(D) The population has skewness or outliers.
(E) The population is not normally distributed.
3. A certain small country has 1,000 farms. Soybeans are grown on exactly 100 of these farms. In order to estimate the total soybean acreage for the country, two plans are proposed.
Plan I: Sample 20 of the 1,000 farms at random, estimate the mean acreage of soybeans per farm in a confidence interval, and multiply both ends of the interval by 1,000 to get an interval estimate of the total.
Plan II: Identify the 100 soybean-growing farms, sample 20 of these at random, estimate the mean acreage of soybeans for soybean-growing farms in a confidence interval, and multiply both ends of the interval by 100 to get an interval estimate of the total.
Which is the best strategy for estimating the total farm acreage of soybeans for the country?
(A) Plan I
(B) Plan II
(C) Either one will work equally well, since both are good and will produce equivalent results
(D) Neither one will work well, since neither estimates the total soybean acreage
(E) Insufficient information
4. Ten students were randomly selected from a high school to take part in a program designed to raise their reading comprehension. Each student took a test before and after completing the program. The mean of the differences between the score after the program and the score before the program is 16. It was decided that all students in the school would take part in this program during the next school year. Let m A denote the mean score after the program and m B denote the mean score before the program for all students in the school. The 95 percent confidence interval estimate of the true mean difference for all students is (9,23). Which of the following statements is a correct interpretation of this confidence interval?
(A) m
A > m
B with probability 0.95
(B) m
A < m
B with probability 0.95
(C) m
A is around 23 and m
B is around 9
(D) For any m
A and m
B with (m
A – m
B ) £
14, the sample result is quite likely
(E) For any m
A and m
B with 9 < (m
A – m
B ) < 23, the sample result is quite likely
5. A large study involving 22,000 male physicians attempted to determine whether aspirin could help prevent heart attacks. In this study, one group of about 11,000 physicians took an aspirin tablet every other day, while a control group took a placebo every other day. After several years, there was statistically significant evidence that physicians in the placebo group had more heart attacks on average. Which of the following statements explains why it would not be appropriate to say that everyone should take an aspirin every other day?
I. The study did not include subjects from other occupations.
II. The study included only males; results may be different in females.
III. Although aspirin may be helpful in preventing heart attacks, it may be harmful in other ways.
(A) I only
(B) II only
(C) III only
(D) II and III only
(E) I, II, and III
6. Referring again to #5, what is meant by the phrase "there was statistically significant evidence that physicians in the placebo group had more heart attacks on average"?
(A) The mean number of heart attacks per patient in the control group exceeded that of the experimental group by an amount that would seldom be produced by chance alone if aspirin had no effect.
(B) The mean number of heart attacks per patient in the experimental group exceeded that of the control group by an amount that would seldom be produced by chance alone if aspirin had no effect.
(C) The physicians in the placebo group had many more heart attacks than the physicians who received aspirin.
(D) The physicians in the placebo group had a much higher rate of heart attacks than the physicians who received aspirin.
(E) None of the above
7. A box of truffles is filled by placing 4 large truffles selected at random from a large batch in which 90 percent are acceptable. Let X denote the number of acceptable truffles in a random sample of 4 truffles taken from the batch. What is the least probable value of X?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
8. A random sample of the costs of dry cleaning orders at a large dry cleaning establishment produces a mean of $18.50 with a standard deviation of $10.05. If there were 20 orders in this sample, with no indication of outliers or strong skewness, which of these gives a 90 percent confidence interval for the average revenue per customer transaction?
(A) $18.50 ±
$2.25
(B) $18.50 ±
$3.70
(C) $18.50 ±
$3.89
(D) $18.50 ±
$10.05
(E) None of the above
9. The scores on the last AP Statistics test were approximately normally distributed with a mean of 75 and a standard deviation of 12. The scores on the U.S. History test were also approximately normally distributed, with a mean of 80 and a standard deviation of 8. Milton scored 81 on the statistics test and 84 on the history test. Relative to the students in each respective course, in which subject did this student do better?
(A) Statistics
(B) History
(C) Equally well in each
(D) There is no basis for comparison (different subjects, different departments)
(E) Cannot be solved without knowing the number of students in each course
10. Referring again to #9, change the problem to assume now that Milton is at a school where all statistics students take U.S. history and vice versa. In other words, the courses have identical student lists. What is Milton’s aggregate z score for the two tests? (To answer this question, you may make the quite unrealistic assumption that students’ test scores in the two courses are independent.)
(A) -0.128
(B) 0.500
(C) 0.693
(D) 0.702
(E) 0.712
11. In a test of the null hypothesis H0: m =10 against the alternative hypothesis Ha: m >10, a sample from a normal population produces a mean of 13.4. The z-score for the sample is 2.12 and the p-value is 0.017. Based on these statistics, which of the following conclusions could be drawn?
(A) There is reason to conclude that m
>10.
(B) Due to random fluctuation, a sample mean exceeds 10 about 48.3 percent of the time.
(C) The error of rejecting the alternative hypothesis occurs about 1.7 percent of the time.
(D) The probability that m
>10 is 0.017.
(E) The probability that m
<10 is 0.983.
12. The distribution of the weights of loaves of bread from a certain bakery follows approximately a normal distribution. Based on a very large sample, it was found that 10 percent of the loaves weighed less than 15.34 ounces, and 20 percent of the loaves weighed more than 16.31 ounces. Which of the following are true concerning the distribution of the weights of the loaves of bread?
(A) m
=15.82, s
=0.48
(B) m
=15.82, s
=0.69
(C) m
=15.87, s
=0.50
(D) m
=15.93, s
=0.46
(E) m
=16.00, s
=0.50
13. The manufacturing process for a certain pharmaceutical yields capsules with varying amounts of the active ingredient. The manufacturer claims that the average amount of active ingredient per capsule is at least 200 mg. In a random sample of 70 capsules, the mean content of the active ingredient is found to be 194.3 mg, with a standard deviation of 21 mg. What is the p-value for the appropriate test?
(A) 0.012
(B) 0.024
(C) 0.050
(D) 0.100
(E) 0.488
14. What are the null and alternative hypotheses for the test described in #13?
(A) H0: m
< 200 mg; Ha: m
³
200 mg
(B) H0: m
£
200 mg; Ha: m
> 200 mg
(C) H0: m
= 200 mg; Ha: m
> 200 mg
(D) H0: m
= 200 mg; Ha: m
< 200 mg
(E) H0: m
= 200 mg; Ha: m
¹
200 mg
15. Suppose that student heights are known to be normally distributed at STA and NCS. Random samples are drawn and heights (in inches) are recorded. STA sample heights are 65, 69, 70, 70, 71, 72, 72, 73, and 75. NCS sample heights are 62, 64, 64, 65, 66, 68, and 69. What can we say?
I. STA sample mean height exceeds that of NCS.
II. STA sample variance for height exceeds that of NCS.
III. There is some evidence that STA’s population standard deviation exceeds that of NCS.
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III
16. The F statistic for #15, computed according to the standard convention, is . . .
(A) 0.749
(B) 1.000
(C) 1.155
(D) 1.335
(E) 1.463
17. The denominator degrees of freedom for the F test in #15 would be . . .
(A) 6
(B) 7
(C) 8
(D) 9
(E) 16
18. In a sample of size 20, the t score corresponding to the 80th percentile would be . . .
(A) 1.282
(B) 1.323
(C) 1.325
(D) 1.328
(E) None of the above
19. One of the most robust tools in the professional statistician’s repertoire is the . . .
(A) 1-sample t test
(B) 2-sample t test
(C) 2-sample F test
(D) 1-sample variance test
(E) None of the above
20. Referring back to #15, the pooled estimator of standard deviation would equal . . .
(A) 2.629
(B) 2.653
(C) 2.659
(D) 2.663
(E) None of the above
21. The conservative degrees of freedom associated with performing a two-sample t test on the data in problem #15 would be . . .
(A) 4
(B) 6
(C) 8
(D) 10
(E) 16
22. The degrees of freedom used in a pooled two-sample t test for #15 would be . . .
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
23. Why do pooled procedures often produce lower p-values and narrower confidence intervals than non-pooled procedures?
(A) In the pooled procedures, df will be higher, which increases the t critical value.
(B) In the pooled procedures, df will be higher, which reduces the t critical value.
(C) The pooled estimator of standard deviation is always less than either of the sample standard deviations.
(D) The pooled estimator of standard deviation is always greater than either of the sample standard deviations.
(E) None of the above
24. Is use of pooled procedures justified in problem #15?
(A) Yes, as shown by the two-sample F test.
(B) Yes, because the difference between sample standard deviations is small.
(C) Yes, provided it is known that the population standard deviations are equal.
(D) No, because the populations are from different schools.
(E) No, because the populations are different genders.
25. All of the z and t procedures that we have studied involve inference about . . .
(A) Sample means (or differences of means)
(B) Population means (or differences of means)
(C) Sample standard deviations
(D) Population standard deviations
(E) None of the above
|
AP Statistics / Mr. Hansen |
Name: _________________________________ |
Test #6 SAMPLE (3/9/1999)
ANSWER SHEET
|
No. |
A |
B |
C |
D |
E |
|
1 |
O |
O |
O |
O |
O |
|
2 |
O |
O |
O |
O |
O |
|
3 |
O |
O |
O |
O |
O |
|
4 |
O |
O |
O |
O |
O |
|
5 |
O |
O |
O |
O |
O |
|
6 |
O |
O |
O |
O |
O |
|
7 |
O |
O |
O |
O |
O |
|
8 |
O |
O |
O |
O |
O |
|
9 |
O |
O |
O |
O |
O |
|
10 |
O |
O |
O |
O |
O |
|
11 |
O |
O |
O |
O |
O |
|
12 |
O |
O |
O |
O |
O |
|
13 |
O |
O |
O |
O |
O |
|
14 |
O |
O |
O |
O |
O |
|
15 |
O |
O |
O |
O |
O |
|
16 |
O |
O |
O |
O |
O |
|
17 |
O |
O |
O |
O |
O |
|
18 |
O |
O |
O |
O |
O |
|
19 |
O |
O |
O |
O |
O |
|
20 |
O |
O |
O |
O |
O |
|
21 |
O |
O |
O |
O |
O |
|
22 |
O |
O |
O |
O |
O |
|
23 |
O |
O |
O |
O |
O |
|
24 |
O |
O |
O |
O |
O |
|
25 |
O |
O |
O |
O |
O |