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AP Statistics
3/11/08
Wood/Myers
Test #11 (Chapter 11-12)
Name ____________________________________________________
Period ______
Honor Pledge _____________________________________________
Part I - Multiple Choice (Questions 1-10) – Bubble the answer of your choice on the scantron form.
1. DDT is an insecticide that accumulates up the food chain. Predator birds can be contaminated with quite
high levels of the chemical by eating many lightly contaminated prey. One effect of DDT upon birds is to
inhibit the production of the enzyme carbonic anhydrase, which controls calcium metabolism. It is believed
that this causes eggshells to be thinner and weaker than normal and makes the eggs more prone to
breakage. (This is one of the reasons why the condor in California is near extinction.) An experiment was
conducted where 16 sparrow hawks were fed a mixture of 3 ppm dieldrin and 15 ppm DDT (a
combination often found in contaminated prey). The first egg laid by each bird was measured, and the
mean shell thickness was found to be 0.19 mm. A “normal” eggshell has a mean thickness of 0.2 mm.
The null and alternative hypotheses are
(a) H 0 :   0.2; H a :   0.2
(b) H 0 :   0.2; H a :   0.2
(c) H 0 : x  0.2; H a : x  0.2
(d) H 0 : x  0.19; H a : x  0.2
(e) H 0 :   0.2; H a :   0.2
2. A significance test allows you to reject a hypothesis H 0 in favor of an alternative Ha at the 5% level of
significance. What can you say about significance at the 1% level?
(a) H 0 can be rejected at the 1% level of significance.
(b)
(c)
(d)
(e)
There is insufficient evidence to reject H 0 at the 1% level of significance.
There is sufficient evidence to accept H 0 at the 1% level of significance.
Ha can be rejected at the 1% level of significance.
The answer can’t be determined from the information given.
3. In a test of H0: µ = 100 against Ha: µ  100, a sample of size 80 produces z = 0.8 for the value of the test
statistic. The P-value of the test is thus equal to
(a) 0.20
(b) 0.40
(c) 0.29
(d) 0.42
(e) 0.21
4. Which of the following is/are correct?
I. The power of a significance test depends on the alternative value of the parameter.
II. The probability of a Type II error is equal to the significance level of the test.
III. Type I and Type II errors make sense only when a significance level has been chosen in
(a) I and II only
(b) I and III only
(c) II and III only
(d) I, II, and III
(e) None of the above gives the complete set of correct responses.
advance.
5. A 95% confidence interval for µ is calculated to be (1.7, 3.5). It is now decided to test the hypothesis H0: µ
= 0 versus Ha: µ  0 at the  = 0.05 level, using the same data as used to construct the confidence
interval.
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Test 11A
(a) We cannot test the hypothesis without the original data.
(b) We cannot test the hypothesis at the  = 0.05 level since the  = 0.05 test is connected to the 97.5%
confidence interval.
(c) We can make the connection between hypothesis tests and confidence intervals only if the sample
sizes are large.
(d) We would reject H0 at level  = 0.05.
(e) We would accept H0 at level  = 0.05.
6. Here's a quote from a medical journal: “An uncontrolled experiment in 17 women found a significantly
improved mean clinical symptom score after treatment. Methodologic flaws make it difficult to interpret
the results of this study.” The authors of this paper are skeptical about the significant improvement
because
(a) there is no control group, so the improvement might be due to the placebo effect or to the fact that
many medical conditions improve over time.
(b) the P-value given was P = 0.03, which is too large to be convincing.
(c) the response variable might not have an exactly Normal distribution in the population.
(d) the study didn’t use enough subjects to achieve any statistically significant findings.
(e) the mean is not resistant.
7. A medical experiment compared the herb echinacea with a placebo for preventing colds. One response
variable was “volume of nasal secretions” (if you have a cold, you blow your nose a lot). Take the average
volume of nasal secretions in people without colds to be  = 1. An increase to
 = 3 indicates a cold. The significance level of a test of H 0 :   1 versus H a :   1 is
(a) the probability that the test rejects H 0 when  = 1 is true.
(b) the probability that the test rejects H 0 when  = 3 is true.
(c) the probability that the test fails to reject H 0 when  = 3 is true.
(d) the probability that the test fails to reject H 0 when  = 1 is true.
(e) none of the above
8. A radio show runs a phone-in survey each morning. One morning the show asked its listeners whether
they would prefer Congress or the president to set policy for the nation. The majority of those phoning in
their responses answered “Congress,” and the station reported the results as statistically significant. We
may safely conclude that
(a) there is deep discontent in the nation with the president.
(b) it is unlikely that, if all Americans were asked their opinion, the result would differ from that obtained
in the poll.
(c) there is strong evidence that the majority of Americans prefer Congress to set national policy.
(d) very few people other than the majority of those phoning in their responses prefer Congress to set
policy for the nation.
(e) that the majority of Americans would actually prefer the president to set policy, because of the biased
method of data collection.
1. An opinion poll asks a random sample of adults whether they favor banning ownership of handguns by
private citizens. A commentator believes that more than half of all adults favor such a ban. The null and
alternative hypotheses you would use to test this claim are
(a) H 0 : pˆ  0.5; H a : pˆ  0.5
(b) H 0 : pˆ  0.5; H a : pˆ  0.5
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Test 11A
(c) H 0 : p  0.5; H a : p  0.5
(d) H 0 : p  0; H a : p  0
(e) None of the above. The answer is _____________________________.
2. Bags of a certain brand of tortilla chips claim to have a net weight of 14 ounces. Net weights actually vary
slightly from bag to bag and are Normally distributed with mean  . A representative of a consumer
advocate group wishes to see if there is any evidence that the mean net weight is less than advertised and
so intends to test the hypotheses
H0:  = 14, Ha:  < 14
To do this, he selects 16 bags of this brand at random and determines the net weight of each. He finds the
sample mean to be x = 13.82 and the sample standard deviation to be s = 0.24.
We conclude that we would
(a) reject H0 at significance level 0.10 but not at 0.05.
(b) reject H0 at significance level 0.05 but not at 0.025.
(c) reject H0 at significance level 0.025 but not at 0.01.
(d) reject H0 at significance level 0.01.
(e) fail to reject H0 at the  = 0.10 level.
3. A Type I error in the previous question would mean
(a) concluding that the bags are being underfilled when they actually aren’t.
(b) concluding that the bags are being underfilled when they actually are.
(c) concluding that the bags are not being underfilled when they actually are.
(d) concluding that the bags are not being underfilled when they actually aren’t.
(e) none of these
4. You are thinking of using a t procedure to test hypotheses about the mean of a population using a significance
level of 0.05. You suspect that the distribution of the population is not Normal and may be moderately
skewed. Which of the following statements is correct?
(a) You should not use the t procedure because the population does not have a Normal distribution.
(b) You may use the t procedure if your sample size is large, say, at least 50.
(c) You may use the t procedure, but you should probably claim only that the significance level is 0.10.
(d) You may not use the t procedure. The t procedures are robust to non-Normality for confidence intervals
but not for tests of hypotheses.
(e) You may use the t procedure if there are no outliers.
5. After once again losing a football game to the archrival, a college’s alumni association conducted
a survey to see if alumni were in favor of firing the coach. An SRS of 100 alumni from the population of all
living alumni was taken. 64 of the alumni in the sample were in favor of firing the coach. Suppose you
wish to see if a majority of living alumni are in favor of firing the coach. The appropriate test statistic is
(a) z  (0.64  0.5)
(0.64)(0.36) 100
(b) z  (0.64  0.5)
(0.5)(0.5) 100
(c) z  (0.64  0.5)
(0.64)(0.36) 64
(d) z  (0.64  0.5)
(0.5)(0.5) 64
(e) t  (0.64  0.5)
(0.5)(0.64) 100
6. We prefer the t procedures to the z procedures for inference about a population mean because
(a) z can be used only for large samples.
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Test 11A
(b) z requires that you know the population standard deviation  .
(c) z requires that you can regard your data as an SRS from the population of interest.
(d) z requires that your population be Normally distributed.
(e) z requires that your observations be independent.
7. Looking online (for example, at espn.go.com) you find the salaries of all 22 players for the Chicago Cubs as
of opening day of the 2005 baseball season. The club total was $87 million, eighth in the major leagues.
Which inference procedure would you use to estimate the average salary of the Cubs players?
(a) one-sample z interval for 
(b) one-sample t interval for 
(c) one-sample t test
(d) one-sample z test
(e) none of these
8. You read in the report of a psychology experiment that “separate analyses for our two groups of 12
participants revealed no overall placebo effect for our student group (mean = 0.08, SD = 0.37,
t(11) = 0.49) and a significant effect for our non-student group (mean = 0.35, SD = 0.37, t(11) = 3.28, p <
0.01).” Are the two values given for the t test statistic correct? (The null hypothesis is that the mean
effect is zero.)
(a) Yes, both are correct.
(b) The t statistic for the student group is correct, but the one for the non-student group is incorrect.
(c) The t statistic for the non-student group is correct, but the one for the student group is incorrect.
(d) Both t statistics are incorrect.
(e) We can’t tell whether either t statistic is correct, because we aren’t given the actual data.
Part II – Free Response (Questions 11-12) – Show your work and explain your results clearly.
9. Acid rain is a serious problem in Canada. In many cases, lakes become so acidified that they cannot
support any significant fish life. One possible (and very costly!) solution is to try to mitigate the effects by
dumping crushed limestone into the lakes. This will neutralize the acidity. The following are actual data
from a study of such an intervention in a lake.
From enormous samples at other control lakes, it is reasonable to assume that under the acidic
conditions the weight of individual fish of a particular age class is Normally distributed with a known mean
µ of 3250 grams (g). One year after the addition of limestone, a sample of 22 fish was taken and the weight
of the individual fish was obtained. Here are the sorted data (g):
1595 1605 1634 2633 2864 2924 3035 3051 3293 3344 3381
3398 3421 3446 3514 3614 3694 3739 3756 3788 3898 3952
Before the analysis began, it was noticed that several fish had abnormally low weights (below 2000 g).
After further investigation it was noted that these fish had ingested pieces of plastic from litterbugs' foam
cups and could not properly digest food. The study's method of analysis was to delete all values less than
2000 g. After deleting such values, x = 3407.6 g. Assume that   370 grams for the weights of fish after
limestone is added.
(a) Carry out an appropriate significance test at the 5% significance level to determine whether the mean
weight of the fish in the lake increased after the limestone was added.
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Test 11A
(b) Would your conclusion in (a) have changed if the outliers had been included in the analysis? Justify
your answer with appropriate statistical evidence.
Chapter 11
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Test 11A
10. When the manufacturing process is working properly, NeverReady batteries have lifetimes that
follow a right-skewed distribution with   7 hours and   0.5 hours. A quality control supervisor
selects a simple random sample of n batteries every hour and measures the lifetime of each. If she is
convinced that the mean lifetime of all batteries produced that hour is less than 7 hours at the 5%
significance level, then all those batteries are discarded.
(a) State appropriate hypotheses for the quality control supervisor to test.
(b) Describe a Type I and a Type II error in this situation, and explain which is more serious.
Since testing the lifetime of a battery requires draining the battery completely, the supervisor wants to
sample as few batteries as possible from each hour’s production. She is considering a sample size of n = 4.
(c) Explain why this sample size may lead to problems in carrying out the significance test from
(a).
(d) Would this sample size give the supervisor sufficient power to detect that the actual mean
lifetime for batteries produced that hour was   6.8 hours? Justify your answer.
(e) Would you recommend that the quality control supervisor use a significance level of   0.01 or
  0.10 in future tests? Explain.
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Test 11A
Part 2: Free Response
Communicate your thinking clearly and completely.
9. Many mutual funds compare their performance with that of a benchmark, an index of the returns on all
securities of the kind the fund buys. The Vanguard International Growth Fund, for example, takes as its
benchmark the Morgan Stanley EAFE (Europe, Australasia, Far East) index of overseas stock market
performance. Here are the percent returns for the fund and for the EAFE from 1982 (the first full year of
the fund’s existence) to 2000.
Does the fund significantly outperform its benchmark? Carry out an appropriate test and state your
conclusion about the fund’s performance.
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Test 11A
10. Mars Inc., makers of M&M’s candies, claims that they produce plain M&M’s with the following
distribution:
Brown: 30%
Red: 20%
Yellow: 20%
Orange: 10%
Green: 10%
Blue: 10%
A bag of plain M&M’s was selected randomly from the grocery store shelf, and the color counts were as
follows:
Brown: 16
Red:
11
Yellow: 19
Orange: 5
Green: 7
Blue: 3
(a) You want to conduct an appropriate test of the manufacturer’s claim for the proportion of yellow
M&M’s. Identify the population and parameter of interest. Then state hypotheses.
(b) State and verify the conditions for performing the significance test.
(c) Calculate the test statistic and the P-value.
(d) What do you conclude about the manufacturer’s claim? Explain.
(e) Based on this sample, construct and interpret a 90% confidence interval for the proportion of yellow
M&M’s candies produced by Mars.
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Test 11A