Download Quiz 11.1A AP Statistics Name: At the bakery where you work

Quiz 11.1A
AP Statistics
Name:
At the bakery where you work, loaves of bread are supposed to weigh 1 pound. From experience, the
weights of loaves produced at the bakery follow a Normal distribution with standard deviation
 = 0.13 pounds. You believe that new personnel are producing loaves that are heavier than 1 pound.
As supervisor of Quality Control, you want to test your claim at the 5% significance level. You weigh
20 loaves and obtain a mean weight of 1.05 pounds.
1. Identify the population and parameter of interest. State your null and alternative hypotheses.
2. Identify the statistical procedure you should use. Then state and verify the conditions required for
using this procedure.
3. Calculate the test statistic and the P-value. Illustrate using the graph provided.
. 50
- 3. 0
3 .0
- . 50
4. State your conclusions clearly in complete sentences.
Chapter 11
Quiz 11.1A
Quiz 11.1B
AP Statistics
Name:
Statistics can help decide the authorship of literary works. Sonnets by an Elizabethan poet are known
to contain an average of  = 6.9 new words (words not used in the poet’s other works). The
distribution of new words in this poet’s sonnets is Normal with standard deviation  = 2.7. Now a
manuscript with five new sonnets has come to light, and scholars are debating whether it is the poet’s
work. The new sonnets contain an average of x = 9.2 words not used in the poet’s known works. We
expect poems by another author to contain more new words than found in the Elizabethan poet’s
poems.
1. Identify the population and parameter of interest. State appropriate hypotheses in both words and
symbols.
2. Identify the appropriate statistical procedure and verify conditions for its use.
3. Calculate the test statistic and the P-value. Illustrate using the graph provided.
.50
-3.0
3 .0
-.50
4. State your conclusions clearly in complete sentences.
Chapter 11
Quiz 11.1A
Quiz 11.2A
AP Statistics
Name:
Here are the Degree of Reading Power (DRP) scores for an SRS of 44 third-grade students from a
suburban school district:
40
26
39
14
42
18
25
43
46
27
19
47
19
26
35
34
15
44
40
38
31
46
52
25
35
35
33
29
34
41
49
28
52
47
35
48
22
33
41
51
27
14
54
45
Suppose that the standard deviation of scores in this school district is known to be  = 11. The
researcher believes that the mean score  of all third-graders in this district is higher than the national
mean, which is 32. Carry out a significance test of the researcher’s belief at the   0.05 significance
level.
Chapter 11
Quiz 11.1A
Quiz 11.2B
AP Statistics
Name:
Here are measurements (in millimeters) of a critical dimension for a random sample of 16 auto engine
crankshafts:
224.120
224.001
224.017
223.982
223.989
223.961
223.960
224.089
223.987
223.976
223.902
223.980
224.098
224.057
223.913
223.999
The data come from a production process that is known to have standard deviation  = 0.060 mm.
The process mean is supposed to be  = 224 mm but can drift away from this target during
production. Is there sufficient evidence to conclude that the mean dimension is not 224 mm? Give
appropriate statistical evidence to support your conclusion.
Chapter 11
Quiz 11.1A
Quiz 11.3A
AP Statistics
Name:
Read the brief newspaper article on using a depression pill to help smokers quit.
Depression Pill Seems to Help Smokers Quit
BOSTON — Taking an antidepression medicine appears to double smokers’ chances
of kicking the habit, a study found. The Food and Drug Administration approved the
marketing of this medicine, called Zyban or bupropion, to help smokers in May. The
results of several studies with the drug, including one published in today’s issue of
the New England Journal of Medicine, were made public then.
The newly published study was conducted on 615 volunteers who wanted to give
up smoking and were not outwardly depressed. They took either Zyban or dummy
pills for 6 weeks. A year later, 23 percent of those getting Zyban were still off
cigarettes, compared with 12 percent in the comparison group.
1. The results of this experiment were significant at the  = 0.05 significance level. In your opinion,
are the results practically significant? Justify your position.
2. To what population can the results of this study be generalized? Explain.
3. Can we conclude that taking Zyban causes people to quit smoking? Justify your answer.
4. In performing a test of significance, the researcher can choose between adopting a fixed
significance level or calculating a P-value. Does it matter which approach is taken? If so, describe
the circumstances when one should use each approach.
Chapter 11
Quiz 11.1A
Quiz 11.3B
AP Statistics
Name:
Emissions of sulfur dioxide by industry set off chemical changes in the atmosphere that result in “acid
rain.” The acidity of liquids is measured by pH on a scale of 0 to 14. Distilled water has pH 7.0, and
lower pH values indicate acidity. “Normal” rain is somewhat acidic, so acid rain is sometimes defined
as rainfall with a pH below 5.0. Suppose that pH measurements of rainfall on different days in a
Canadian forest follow a Normal distribution with standard deviation  = 0.5. A sample of n days
finds that the mean pH is x = 4.8. Is this good evidence that the mean pH  for all rainy days is less
than 5.0?
1. Use the computer applet below to help you carry out a significance test at the   0.05 level.
2. The screen shots from the computer applet below are meant to illustrate a statistical lesson.
Describe that lesson in a clearly written sentence or two.
Chapter 11
Quiz 11.1A
Quiz 11.4A
AP Statistics
Name:
In a criminal trial, the defendant is held to be innocent until shown to be guilty beyond a reasonable
doubt. If we consider hypotheses
H0: defendant is innocent
Ha: defendant is guilty
we can reject H0 only if the evidence strongly favors Ha.
1. Is this goal better served by a test with  = 0.20 or a test with  = 0.01? Explain your answer.
2. Make a diagram that shows the truth about the defendant, and the possible verdicts and that
identifies the two types of error. Which type of error is more serious?
3. Explain what is meant by the power of the test in this setting.
Chapter 11
Quiz 11.1A
Quiz 11.4B
AP Statistics
Name:
Many suppliers use inspection procedures for quality control. For example, a contract between a
manufacturer and a consumer for light bulbs may specify that the mean lifetime of the bulbs must be at
least 1000 hours. As part of the quality assurance program, the manufacturer will institute an
inspection program for each day's production of 10,000 units. An ordinary testing procedure is difficult
since 1000 hours is over 41 days! Since the lifetime of a bulb decreases as the voltage applied
increases, a common procedure is to perform an accelerated lifetime test in which the bulbs are lit
using 400 volts (compared to the usual 110 volts). At such a voltage, a 1000-hour bulb will last (on
average) only 3 hours. This is a well-known procedure, and both sides have agreed that the results
from the accelerated test will be a valid indicator of lifetime of the bulb. The manufacturer proposes
the following procedure:
Hypotheses: H0: µaccelerated = 3
Ha: µaccelerated < 3
Sample 100 bulbs at random per day.
Reject all lots whose P-value of the test-statistic is less than 0.05.
In other words, the manufacturer will ship a day’s production unless the null hypothesis is rejected.
1. Describe a Type I and a Type II error in this setting. What are the consequences associated with
each type of error?
2. Explain clearly two different things that could be done to increase the power of the proposed test
procedure.
Chapter 11
Quiz 11.1A