AP Statistics
3/27/01 Coley / P. Myers / Wylder
Test #11 (Chapter 11) Name ______
Part I - Multiple Choice (Questions 1-10) - Circle the answer of your choice.
1. When a virus is placed on a tobacco leaf, small lesions appear on the leaf. To compare the mean number of lesions produced by two different strains of virus, one strain is applied to half of each of 8 tobacco leaves, and the other strain is applied to the other half of each leaf. The strain that goes on the right half of the tobacco leaf is decided by a coin flip. The lesions that appear on each half are then counted. The data are given below.
Leaf
/ 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8Strain 1 / 31 / 20 / 18 / 17 / 9 / 8 / 10 / 7
Strain 2 / 18 / 17 / 14 / 11 / 10 / 7 / 5 / 6
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 lesions per leaf produced by the two strains?
(a) 7
(b) 8
(c) 11
(d) 14
(e) 16
2. Which of the following is a criterion for choosing a t-test rather than a z-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 sample may not have been a simple random sample.
(d) The population is not normally distributed.
(e) The sample size is less than 100.
3. What is the critical value t* which satisfies the condition that the t distribution with 8 degrees of freedom has probability 0.10 to the right of t*?
(a) 1.397
(b) 1.282
(c) 2.89
(d) 0.90
(e) cannot be determined
4. In a test for acid rain, an SRS of 49 water samples showed a mean pH level of 4.4 with a standard deviation 0f 0.35. Find a 90% confidence interval estimate for the mean pH level.
(a) 4.4 0.01
(b) 4.40.08
(c) 4.40.32
(d) 4.40.35
(e) 4.40.58
5. The process of producing pain-reliever tablets with varying amounts of the active ingredient. It is claimed that the average amount of active ingredient per tablet is at least 200 milligrams. The Consumer Watchdog Bureau tests a random sample of 70 tablets. The mean content of the active ingredient for this sample is 194.3 milligrams with a standard deviation of 21 milligrams. What is the approximate p-value for the appropriate test?
(a) 0.012
(b) 0.024
(c) 0.050
(d) 0.100
(e) 0.488
6. The number of accidents per day at a large factory is noted for each of 64 days with a mean of 3.58 and a standard deviation of 1.52. With what degree of confidence can we assert that the mean number of accidents per day at the factory is between 3.20 and 3.96?
(a) 48%
(b) 63%
(c) 90%
(d) 95%
(e) 99%
7. In one experiment to test the effect of alcohol on large motor skills, volunteers were randomly placed in two groups, A and B. Everyone in group A drank 2 ounces of alcohol, and 20 minutes later everyone in both groups was timed on a manual dexterity test. The average completion times for the group A and B volunteers were 38 and 31 seconds, respectively. The 90% confidence interval estimate for the mean difference is (3,11). If and are the true mean completion times, respectively, for people who have and have not drunk 2 ounces of alcohol, how many of the following statements are reasonable conclusions?
I. with probability 0.90
II. There is a 0.90 probability that .
III. The interval (3,11) was calculated by a method that gives correct result (for where lies) in 90% of all possible samples.
IV. We are 90% confident that lies between 3 and 11 seconds.
(a) None
(b) One
(c) Two
(d) Three
(e) Four
8.
(a)
(b)
(c)
(d)
(e)
9.
(a)
(b)
(c)
(d)
(e)
10.
(a)
(b)
(c)
(d)
(e)
Part II – Free Response (Questions 11-12) – Show your work and explain your results clearly.
11. Researchers want to determine whether training increases the capability of people to correctly predict outcomes of coin tosses. Each of twenty people is asked to predict the outcome (head or tails) of 100 independent tosses of a fair coin. After training, they are retested with a new set of 100 tosses. (All 40 sets of 100 tosses are independently generated.) Since the coin is fair, the probability of a correct guess is 0.5 on each toss. The numbers correct for each of the 20 people were as follows.
Score Before Training (number correct) / 46 / 48 / 50 / 54 / 54 / 54 / 54 / 54 / 54 / 54 / 55 / 56 / 57 / 58 / 58 / 61 / 61 / 63 / 64 / 65Score After Training (number correct) / 61 / 62 / 53 / 46 / 50 / 52 / 53 / 59 / 60 / 61 / 55 / 59 / 55 / 50 / 56 / 58 / 64 / 57 / 61 / 54
a. Do the data suggest that after training people can correctly predict coin toss outcomes better than the 50% expected by chance guessing alone?
Give appropriate statistical evidence to support your conclusion.
b. Does the statistical test that you completed in part (a) provide evidence that this training is effective in improving a person’s ability to predict coin toss outcomes?
If yes, justify your answer. If no, conduct an appropriate analysis that would allow you to determine whether or not the training is effective.
c. Would knowing a person’s score before training be helpful in predicting his or her score after training? Justify your answer.
12. Several different types of cheese are produced in the shape of a wheel. Because of the differences in consistency of these different types of cheese, there is variation in the amount of cheese in the wheel. Cam Embert wishes to determine if there is a significant difference, at the 8% level, between Gouda cheese and Brie Cheese. She randomly samples 18 wheels of Gouda and finds the mean is 1.3 pounds with a standard deviation of 0.31 pound and 13 wheels of Brie and finds a mean of 0.95 pounds and a standard deviation of 0.26 pound. What is the probability that Cam will reject the hypothesis of equality when in fact the true difference in the means is 0.15?