Download Chapter 8-10 Review Multiple Choice: Identify the choice that best

Chapter 8-10 Review
Multiple Choice: Identify the choice that best completes the statement or answers the question.
Scenario 10-6
Child within three years?
YES
NO
Divorced within five
YES
83
52
years?
NO
137
128
Total
220
180
A sociologist hypothesizes that couples who have a child within the first three years of marriage are more likely to divorce. From city
records, she selects a random sample of 400 couples who were both between the ages of 20 and 25 when they married. She compared
the divorce rate of couples who had a child within the first three years of marriage to the divorce rate of couples who did not. Here are
her results:
1. Use Scenario 10-6. Let p1 = proportion of couples that had a child within the first three years and were divorced within five years
and p2 = proportion of couples that did not have a child within the first three years and were divorced within five years. We wish to
test the hypotheses
statistic?
A.
D.
2.
A.
B.
C.
D.
E.
vs.
. Which of the following is the appropriate expression for the test
B,
C.
E.
Use Scenario 10-6. The P-value for this onethere is evidence of an association between divorce rate and having children early in a marriage.
having more children increases the risk of divorce during the first 5 years of marriage.
If you want to decrease your chances of getting divorced, it is best to marry later in life.
If you want to decrease your chances of getting divorced, it is best not to have children.
If you want to decrease your chances of getting divorced, it is best to wait several years before
having children.
3.
thinks that the apartments are smaller than advertised. They hire an engineer to measure a sample of apartments to test their suspicion.
The appropriate null and alternative hypotheses, H0 and Ha, for this test are
A. H0: µ = 1250 and Ha: µ ≠ 1250.
B. H0: µ = 1250 and Ha: µ < 1250.
C. H0: µ = 1250 and Ha: µ > 1250.
D. H0: µ < 1250 and Ha: µ = 1250.
E. cannot be specified without knowing the size of the sample used by the
engineer.
4. You have data on rainwater collected at 16 locations in the Adirondack Mountains of New York State. One measurement is the
acidity of the water, measured by pH on a scale of 0 to 14 (the pH of distilled water is 7.0). Which inference procedure would you use
to estimate the average acidity of rainwater in the Adirondacks?
A. one-sample z interval for
B/ one-sample t interval for
C. one proportion z-test
D. one-sample t test
E. one-sample z test
5.
A.
C.
E.
Because t procedures are robust, the most important condition for their use is
the population standard deviation is known.
B. the population distribution is approximately Normal.
the data can be regarded as a random from the population.
D. np and n(1 – p) are both at least 10.
all values in the sample are within two standard deviations of the mean.
6. A researcher studying reaction time of drivers states that, “A 95% confidence interval for the mean time it takes for a driver to
apply the brakes after seeing the brake lights on a vehicle in front of him is 1.2 to 1.8 seconds. What are the point estimate and margin
of error for this interval?
A. Point estimate = 1.2 seconds; margin of error = 0.6 seconds.
B. Point estimate = 1.2 seconds; margin of error = 0.3
seconds.
C. Point estimate = 1.5 seconds; margin of error 95%.
D. Point estimate = 1.5 seconds; margin of error = 0.6
seconds.
E. Point estimate = 1.5 seconds; margin of error = 0.3 seconds.
Scenario 10-7 Some researchers have conjectured that stem-pitting disease in peach tree seedlings might be controlled with weed and
soil treatment. An experiment was conducted to compare peach tree seedling growth with soil and weeds treated with one of two
herbicides. In a field containing 20 seedlings, 10 were randomly selected from throughout the field and assigned to receive Herbicide
A. The remaining 10 seedlings were to receive Herbicide B. Soil and weeds for each seedling were treated with the appropriate
herbicide, and at the end of the study period, the height (in centimeters) was recorded for each seedling. A box plot of each data set
showed no indication of non-Normality. The following results were obtained:
S (cm)
(cm)
Herbicide A
94.5
10
Herbicide B
109.1
9
7. Use Scenario 10-7. A 95% confidence interval for
conservative value for degrees of freedom.)
A.
B.
is given by which of the following expressions? (Use the
C.
D.
E.
8.
Use Scenario 10-7. Suppose we wished to determine if there tended to be a significant difference in mean height for the seedlings
treated with the different herbicides. To answer this question, we decide to test the hypotheses H0:
A. 14.60
vs. Ha:
. Based on our data, which of the following is the value of test statistic?
B. 7.80
C. 3.43
D. 2.54
E. 1.14
9. An SRS of 100 postal employees found that the average time these employees had worked for the postal service was J = 7 years
with standard deviation s = 2 years. Suppose we are not sure if the population distribution is normal. In which of the following
circumstances would use of the t procedure yield misleading results?
A. A histogram of the data shows moderate skewness.
B. A stemplot of the data shows a uniform distribution.
C. The sample standard deviation is large.
D. A histogram of the data shows strong skewness. E. none of
the above
Scenario 8-3 After a college’s football team once again lost a football game to the college’s arch rival, the 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. Sixty-four of the alumni in the sample were in favor of firing the coach. Let p represent the proportion of all living alumni
who favor firing the coach.
10. Use Scenario 8-3. Which of the following is closest to the sample size you would need to estimate p with a margin of error of
0.05 with 95% confidence? Use 0.5 as an approximation of p.
A. 269
B. 385
C. 538
D. 768
E. 1436
11. The government claims that students earn an average of $4500 during their summer break from studies. A random sample of
students gave a sample average of $3975, and a 95% confidence interval was found to be $3525 < µ < $4425. Which of the following
is a correct interpretation of 95% confidence?
A. if the study were to be repeated many times, there is a 95% probability that the true average summer earnings is not $4500 as
the government claims.
B. because our specific confidence interval does not contain the value $4500 there is a 95% probability that the true average
summer earnings is not $4500.
C. if we were to repeat our survey many times, then about 95% of all the confidence intervals will contain the value $4500.
D. if we repeat our survey many times, then about 95% of our confidence intervals will contain the true value of the average
earnings of students.
E. there is a 95% probability that the true average earnings are between $3525 and $4425 for all students.
12. An ecologist studying differences in populations of a certain species of lizards on two different islands collects lizards in live
traps, weighs them, and then releases them again. (He marks them so he won’t weigh the same lizard twice). During one study
period, he collects the following data. All weights are in grams.
n
Mean (gm)
Std. Dev. (gm)
Sheep Island
24
46.5
5.97
Pig Island
30
44.2
4.24
Which of the following is the correct expression for the test statistic to test the hypothesis that the mean weights on the two islands are
equal?
A.
B.
C.
D.
E.
13. What is the critical value t* for a 90% confidence interval when n = 15?
A. 1.645
B. 1.753
C. 1.761
D. 1.960
E. 2.145
14. A quality control inspector is testing microprocessor chips made during a single day by a new machine to determine the
proportion of defective chips. She selects an SRS of 80 chips from the 3000 chips produced by the machine on that day. It turns out
that six of the chips are defective. Which of the following conditions for constructing a confidence interval for the proportion of
defective chips has been violated?
A.
B. An SRS has been taken from the population of interest.
C. The population is at least 10 times the size of the sample.
E. There appear to be no violations.
D.
The population is approximately Normally distributed.
15. Twenty-five seniors from a large metropolitan area school district volunteer to allow their Math SAT test scores to be used in a
study. These twenty-five seniors had a mean Math SAT score of J = 450. Suppose we know that the standard deviation of the
iors in
the population of
seniors computed from these data is
A. 450 ± 32.9.
B. 450 ± 39.2.
C. 450 ± 164.5.
D. not trustworthy because the conditions for this inference procedure have not been met.
E. 90% likely to contain the unknown mean math SAT score of all seniors in the district.
Scenario 9-2 Your teacher claims to produce random numbers from 1 to 5 (inclusive) on her calculator, but you’ve been keeping
track. In the past 80 rolls, the number “five” has come up only 8 times. You suspect that the calculator is producing fewer fives than
it should. Let p = actual long-run proportion of five’s produced by the calculator.
16.
A.
D.
Use Scenario 9-2. The hypotheses for testing the teacher’s claim are:
B.
C.
D.
17. If a significance test gives P-value 0.005,
A. the null hypothesis is very likely to be true.
B. we do not have convincing evidence in favor of the null hypothesis.
C. we do not have convincing evidence against the null hypothesis.
D. we do have convincing evidence against the null
hypothesis.
E. we have convincing evidence in favor of the alternative hypothesis.
18. Which of the following statements 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. Error probabilities can be expressed only when a significance level has been specified.
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.
Scenario 10-10 A researcher wishes to compare the effect of two stepping heights (low and high) on heart rate in a step-aerobics
workout. He randomly assigns 50 adult volunteers to two groups of 25 subjects each. Group 1 does a standard step-aerobics workout
at the low height. The mean heart rate at the end of the workout for the subjects in group 1 was
standard deviation of
beats per minute with a
beats per minute. Group 2 did the same workout but at the high step height. The mean heart rate at the
end of the workout for the subjects in group 2 was
beats per minute with a standard deviation of
beats per
minute. Assume the two groups are independent and both data sets are approximately Normal. Let µ1 and µ2 represent the mean heart
rates we would observe for the entire population represented by the volunteers if all members of this population did the workout using
the low or high step height, respectively.
19.
Use Scenario 10-10. The P-value in the previous question was produced by a calculator, using the software estimate of 43.97
degrees of freedom. If we used the more conservative value of the smaller of
or
, how would the P-value change
for the same data?
A. It would be smaller.
B. It would be larger.
C. It would not change, since the test statistic’s value is not influenced by the degrees of freedom.
D. Since the P-value depends on the value of a random variable (the sample mean), we can’t predict whether it will be larger,
smaller, or the same.
E. Whether it’s larger, smaller, or the same depends on what level of significance we choose.
20. Use Scenario 10-10. The researcher decides to test the hypotheses
vs.
level and produces a P-value of 0.0475. Which of the following is a correct interpretation of this result?
A. The probability that the difference
is 0.0475.
at the α = 0.05
B. The probability that this test resulted in a Type II error is 0.0475.
C. If this test were repeated many times, we would make a Type I error 4.75% of the time.
D. If the null hypothesis is true, the probability of getting a difference in sample means as far or farther from 0 as the
difference in our samples is 0.0475.
E. If the null hypothesis is false, the probability of getting a difference in sample means as far or farther from 0 as the
difference in our samples is 0.0475.
21. 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. the majority of those phoning in their responses prefer Congress to set policy for the nation, but know very little about
anyone else.
E. that the majority of Americans would actually prefer the president to set policy, because of the biased method of data
collection.
22. A traffic consultant wants to estimate the proportion of cars on a certain street that have more than two occupants. She stands at
the side of the road for two hours on a weekday afternoon and flips a coin each time a car approaches. If the coin comes up heads, she
counts the number of occupants in the car. After two hours, she has counted 103 cars, 15 of which had more than two occupants.
Which condition for constructing a confidence interval for a proportion has she failed to satisfy?
A.
B.
C.
D. The sample is less than 10% of the population.
interest.
E. The data is an SRS from the population of
23.
An agricultural researcher plants 25 plots with a new variety of corn. A 90% confidence interval for the average yield for these
h of the following would produce a confidence interval with a smaller
margin of error than this one?
A. Using a 95% confidence level.
B. Reducing bias in the study design. C. Planting 100 plots, rather than 25.
D. Using 25 control plots with an old variety of corn.
E. None of the above.
Scenario 10-2 An SRS of 100 flights by Nite-flite Airlines showed that 64 were on time. An SRS of 100 flights by Waxwing Airlines
showed that 80 were on time. Let pN be the proportion of on-time flights for all Nite-flite Airline flights, and let pW be the proportion
of all on-time flights for all Waxwing Airlines flights.
24.
Use Scenario 10-2. When calculating the test statistic, what expression would they use to estimate the standard deviation of the
sampling distribution of the difference in proportions,
A.
B.
C.
25.
A.
?
D.
E.
Use Scenario 10-2. A 95% confidence interval for the difference pA – pW is
B.
C.
D.
E.
26. An experiment to test the effectiveness of regular treatments with fluoride varnish to reduce tooth decay involved 36 volunteers
who had half of their teeth—the right side or left side, determined by a coin flip—painted with a fluoride varnish every six month for
5 years. At the end of the treatments, the number of new cavities during the treatment period was compared on treatment (fluoride
varnish) side versus the control (no fluoride varnish) side. The appropriate statistical test for analyzing the results of this experiment is
A. One-sample z-test of proportions.
B. Two-sample z-test for difference of proportions.
C. One-sample t-test on
paired data.
D. Two-sample t-test for difference of means.
E. Two-sample z-test for difference of means.
27. A level C confidence interval is
A. any interval with margin of error ± C.
B. an interval computed from sample data by a method that has probability C of producing an interval containing the true value of
the parameter of interest.
C. an interval with margin of error ± C that is also correct C% of the time.
D. an interval computed from sample data by a method that guarantees that the probability the interval computed contains the
parameter of interest is C.
E. an interval computed from sample data that has probability (1 – C) of not containing the parameter of interest.
28. A Type II error is
A. rejecting the null hypothesis when it is true.
B. failing to reject the null hypothesis when it is false.
C. incorrectly specifying the null hypothesis. D. incorrectly specifying the alternative hypothesis. E. more serious than a
T
Type I error.
29. To estimate µ, the mean salary of full professors at American colleges and universities, you obtain the salaries of a random
sample of 400 full professors. The sample mean is
and the sample standard deviation is s = $4400. A 99% confidence
interval for µ is
A. $73,220 ± 11,440.
B. $73,220 ± 567.
C. $73,220 ± 431.
D. $73,220 ± 28.6.
E. none of these.
30. You have two large bins of marbles. In bin A, 40% of the marbles are red. In bin B, 52% of the marbles are red. You select a
simple random sample of 30 marbles from bin A and 40 marbles from bin B. What is the probability that the proportion of red
marbles in the sample from bin A is greater than the proportion of red marbles from bin B?
A. nearly zero
B. 0.0010
C. 0.1190
D. 0.1357
E. 0.1562
31. 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 provided your sample size is at least thirty.
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. t procedures are robust to nonnormality for confidence intervals but not for tests of
hypotheses.
E. You may use the t procedure provided that there are no outliers.
32. A radio talk show host with a large audience is interested in the proportion
of adults in his listening area that think the
drinking age should be lowered to 18. To find out, he poses the following question to his listeners: “Do you think that the drinking age
should be reduced to 18 in light of the fact that 18-year-olds are eligible for military service?” He asks listeners to phone in and vote
“yes” if they agree the drinking age should be lowered and “no” if not. Of the 100 people who phoned in, 70 answered “yes.” Which
of the following assumptions for inference about a proportion using a confidence interval has been violated?
A. The population is at least 10 times as large as the sample.
B.
C.
D. The data are an SRS from the population of interest.
E. There appear to be no violations.
Scenario 8-4 A sociologist is studying the effect of having children within the first two years of marriage on the divorce rate. Using
hospital birth records, she selects a random sample of 200 couples that had a child within the first two years of marriage. Following up
on these couples, she finds that 80 couples are divorced within five years.
33. Use Scenario 8-4. A 90% confidence interval for the proportion p of all couples that had a child within the first two years of
marriage and are divorced within five years is
A. 0.40 ± 0.004.
B. 0.40 ± 0.035.
C. 0.40 ± 0.044.
D/ 0.40 ± 0.057.
E/ 0.40 ± 0.068.
34. The survey in the previous question was conducted by calling land-line telephones, and those conducting the survey are
concerned about the possibility of undercoverage, since some people do not own a phone or own only a cell phone. Which of the
following is the best way for them to correct for this source of bias?
A. Use a lower confidence level, such as 80%.
B. Use a higher confidence level, such as 99%.
C. Take a larger
sample.
D. Use a t-interval instead of a z-interval.
E. Throw this sample out and start over again with a better sampling
method.
35. In an opinion poll, 25% of a random sample of 200 people said that they were strongly opposed to having a state lottery. The
standard error of the sample proportion is approximately
A. 0.0094
B. 0.0306
C. 0.0353
D. 0.2500
E. 6.1237
36. You are constructing a 90% confidence interval for the difference of means from simple random samples from two independent
populations. The sample sizes are
and
. You draw dot plots of the samples to check the normality condition for twosample t-procedures. Which of the following descriptions of those dot plots would suggest that it is safe to use t-procedures?
I. The dot plot of sample 1 is roughly symmetric, while the dot plot of sample 2 is moderately skewed left. There are no outliers.
II. Both dot plots are roughly symmetric. Sample 2 has an outlier. III. Both dot plots are strongly skewed to the right. There are no
outliers.
A. I only
B. II only
C. I and II
D. I, II, and III,
E. t-procedures are not recommended in any of these cases
37. In a test of H0: p = 0.7 against Ha: p
0.7, a sample of size 80 produces z = 0.8 for the value of the test statistic. Which of the
following is closest to the P-value of the test?
A. 0.2090
B. 0.2119
C. 0.4238
D. 0.4681
E. 0.7881
38. A student’s AP statistics project involves comparing the time it takes a student to complete a set of 25 basic trinomial factoring
problems while listening to either rap music or country music. Twelve students are timed on two different sets of problems and the
order of both which set of problems he does first and which music he listens to first are randomized. The resulting data is thus paired,
with each student acting as his own “pair.” Which of the following conditions is required to perform a t-test on these paired data?
A. The distribution of times for all students on each set of problems must be approximately Normal.
B. The distribution of times for all students while listening to each type of music must be approximately Normal.
C. The distribution of times for all 24 sets of problems (12 students are taking 2 tests each) must be approximately Normal.
D. The distribution of differences between each individual student’s times on each of the two tests (time with rap – time with
country) must be approximately Normal.
E. More than one of the four conditions above must be satisfied.
39.
A.
B.
C.
D.
E.
Which of the following has the highest probability?
Randomly selecting a value greater than 3 from a standard Normal distribution.
Randomly selecting a value greater than 3 from a t-distribution with 4 degrees of freedom.
Randomly selecting a value greater than 3 from a t-distribution with 20 degrees of freedom.
Randomly selecting a value less than 3 from a standard Normal distribution.
Randomly selecting a value less than 3 from a t-distribution with 20 degrees of freedom.
A 95% confidence interval for p, the proportion of all shoppers at a large grocery store who purchase cookies, was found to be (0.236,
0.282).
40. Use Scenario 8-1. Which of the following would be true about a 98% confidence interval constructed using the same data?
A. The interval would be wider, because the standard error would be larger.
B. The interval would be narrower, because the standard error would be smaller.
C. The interval would be wider, because the critical z* would be larger.
D. The interval would be narrower, because the critical z* would smaller.
E. The interval would be about the same width, because the standard error would be smaller, but the critical z* would be larger.
Short Answer
1. Nicotine patches are often used to help smokers quit. Does giving medicine to fight depression also help? A randomized doubleblind experiment assigned 244 smokers to receive nicotine patches and another 245 to receive both a patch and the antidepressant drug
bupropion. After a year, 40 subjects in the nicotine patch group had abstained from smoking, as had 87 in the patch-plus-drug group.
(a) Construct and interpret a 99% confidence interval for the difference in the proportion of smokers who abstain when using
buproprion and a nicotine patch and the proportion who abstain when using only a patch.
(b) Based only on this interval, do you think that the difference in proportion of abstaining smokers is significant? Justify
your answer.
2. The germination rate of seeds is defined as the proportion of seeds that , when properly planted and watered, sprout and grow. A
certain variety of grass seed usually has a germination rate of 0.80, and a company wants to see if spraying the seeds with a chemical
that is known to change germination rates in other species will change the germination rate of this grass species. They spray 400
seeds with the chemical, and 307 of the seeds germinate. This produces a 95% confidence interval for the proportion of seeds that
germinate of (0.726, 0.809).
(a) Suppose the company conducted a test of
against the alternative
= 0.05. Use the
confidence interval to determine whether this test would reject or fail to reject the null hypothesis. Explain your reasoning.
(b) Find the P-value for the test described in part (a). You do not need to present a complete significance test. Explain what
the P-value measures in the context of the problem.
4. When the manufacturing process is working properly, NeverReady batteries have lifetimes that follow a slightly right-skewed
distribution with
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) Define the parameter of interest and state appropriate hypotheses for the quality control supervisor to test.
(b) 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. Explain why this sample size may lead
to problems in carrying out the significance test from (a).
(c) Describe a Type I and a Type II error in this situation and the consequences of each.
(d)The quality control officer is considering changing the significance level of the test to 1%. Discuss the impact this might
have on error probabilities and the power of the test, and describe the practical consequences of this change.
5. Is the ratio of male births to female births even? A simple random sample of births in a major metropolitan area found 1345 boys
among 2546 firstborn children. A 99% confidence interval for
= the proportion of male births in this population is given by
(0.5028, 0.5538).
(a) Use the confidence interval to draw a conclusion about the hypothesis
against
. Be sure to indicate
the appropriate significance level.
(b) What information is provided by the confidence interval that would not be provided by a test of significance alone?
6. Daphnia pulicaria is a water flea—a small crustacean that lives in lakes and is a major food supply for many species of fish.
When fish are present in the lake water, they release chemicals called kairomones that induce water fleas to grow long tail spines that
make them more difficult for the fish to eat. One study of this phenomenon compared the relative length of tail spines in Daphnia
pulicaria when kairomones were present to when they were not. Below are data on the relative tail spine lengths, measured as a
percentage of the entire length of the water flea.
Relative tail spine length
n
s
Fish kairomone present
214
37.26
4.68
Fish kairomone absent
152
30.67
4.19
(a) Do the data provide convincing evidence that the mean relative tail spine length of Daphnia is longer in the presence of
fish kairomones? Assume the conditions for inference have been met.
(b) What additional information would you need to confirm that the conditions for this test have been met?
7. A university health services physician is concerned about how much sleep freshman are getting in the first few months of school.
She asks a simple random sample of 20 students how much sleep they got the previous night and constructs a 95% confidence interval
for the mean amount of sleep in hours.
(a) Discuss whether this study meets the necessary conditions for constructing a confidence interval. If you think one of the
conditions has not been met, what additional information would be required or what change in the study would you recommend?
(b) If, instead of constructing a 95% confidence interval, the physician constructed a 90% confidence interval, would the 90%
interval be wider, narrower, or the same width as the 95% interval? Explain.
(c) How would the width of confidence interval change if the physician took a larger sample? Explain.
8. A recent poll found that “433 of the 1548 randomly-selected adults questioned felt that unemployment compensation should be
extended an additional six months while the country is in it current economic downturn.” We want to use this information to construct
a 95% confidence interval to estimate the proportion of the U.S. adults who feel this way.
(a) State the parameter our confidence interval will estimate.
(b) Identify each of the conditions that must be met to use this procedure, and explain how you know that each one has been
satisfied.
(c) Find the appropriate critical value and the standard error of the sample proportion.
(d) Give the 95% confidence interval.
(e) Interpret the confidence interval constructed in part (d) in the context of the problem.
(f) Suppose you wanted to estimate the proportion of people who feel that unemployment compensation should be expanded
with 95% confidence to within ± 1.5%. Calculate how large a sample you would need.
(g) If you wanted to have a margin of error of ±1.5% with 99% confidence, would your sample have to be larger, smaller, or
the same size as the sample in part (f)? Explain.
(h) This poll was conducted by randomly calling cell phone numbers. Explain how undercoverage could lead to a biased
estimate in this case, and speculate about the direction of bias.
9. Lumber companies dry freshly-cut wood in kilns before selling it. As a result of the drying process a certain percentage of the
boards become “checked,” which means that cracks develop at the ends of the boards. The current drying procedure for 1” x 4” red
oak boards is known to produce cracks in 16% of the boards. The drying supervisor at a lumber company wants to test a new method
to determine if fewer boards crack.
(a) Define the parameter of interest and write the appropriate null and alternative hypotheses for the test that is described.
Suppose the drying supervisor uses the new method on an SRS of boards and finds that the sample proportion of checked boards is
0.11, which produces a P-value of 0.027.
(b) Interpret the P-value in the context of the problem.
(c) What conclusion would you draw at the α = 0.05 level? At the α = 0.01 level?