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essentials of statistics

The Basic Practice Of Statistics 5th Edition David S Moore - Solutions

How much oil? How much oil wells in a given field will ultimately produce is key information in deciding whether to drill more wells. Here are the estimated total amounts of oil recovered from 64 wells in the Devonian Richmond Dolomite area of the Michigan basin, in thousands of barrels:22 21.71
Weeds among the corn. Velvetleaf is a particularly annoying weed in cornfields.It produces lots of seeds, and the seeds wait in the soil for years until conditions are right. How many seeds do velvetleaf plants produce? Here are counts from 28 plants that came up in a cornfield when no herbicide
Fungus in the air. The air in poultry-processing plants often contains fungus spores. Inadequate ventilation can affect the health of the workers. The problem is most serious during the summer. To measure the presence of spores, air samples are pumped to an agar plate and “colony-forming units
Growing trees faster. The concentration of carbon dioxide (CO2) in the atmosphere is increasing rapidly due to our use of fossil fuels. Because plants use CO2 to fuel photosynthesis, more CO2 may cause trees and other plants to grow faster.An elaborate apparatus allows researchers to pipe extra CO2
Genetic engineering for cancer treatment, continued. Another outcome in the cancer experiment described in Exercise 17.35 is measured by a test for the presence of cells that trigger an immune response in the body and so may help fight cancer. Here are data for the 11 subjects: counts of active
Genetic engineering for cancer treatment. Here’s a new idea for treating advanced melanoma, the most serious kind of skin cancer. Genetically engineer white blood cells to better recognize and destroy cancer cells, then infuse these cells into patients. The subjects in a small initial study were
An outlier’s effect. A good way to judge the effect of an outlier is to do your analysis twice, once with the outlier and a second time without it. The data in Exercise 17.32 follow a Normal distribution quite closely except for one patient with HAV angle 50 degrees, a high outlier.(a) Find the
An outlier’s effect. Our bodies have a natural electrical field that is known to help wounds heal. Does changing the field strength slow healing?Aseries of experiments with newts investigated this question. In one experiment, the two hind limbs of 12 newts were assigned at random to either
A big toe problem. Hallux abducto valgus (call it HAV) is a deformation of the ST EP big toe that often requires surgery. Doctors used X-rays to measure the angle (in degrees) of deformity in 38 consecutive patients under the age of 21 who came to a medical center for surgery to correctHAV. The
Learning Blissymbols. Blissymbols are pictographs (think of Egyptian hieroglyphics)sometimes used to help learning-disabled children. In a study of computerassisted learning, 12 normal-ability schoolchildren were assigned at random to each of four computer learning programs. After they used the
The conductivity of glass. How well materials conduct heat matters when designing houses, for example. Conductivity is measured in terms of watts of heat power transmitted per square meter of surface per degree Celsius of temperature difference on the two sides of the material. In these units,
The placebo effect. The placebo effect is particularly strong in patients with Parkinson’s disease. To understand the workings of the placebo effect, scientists measure activity at a key point in the brain when patients receive a placebo that they think is an active drug and also when no
Calcium and blood pressure. In a randomized comparative experiment on the effect of calcium in the diet on blood pressure, researchers divided 54 healthy white males at random into two groups. One group received calcium; the other, a placebo.At the beginning of the study, the researchers measured
Reading scores in Atlanta. The Trial Urban District Assessment (TUDA) is a government-sponsored study of student achievement in large urban school districts.TUDA gives a reading test scored from 0 to 500. A score of 243 is a “basic” reading level and a score of 281 is “proficient.” Scores
Body mass index of young women. In Example 14.1 (page 360) we developed a 95% z confidence interval for the mean body mass index (BMI) of women aged 20 to 29 years, based on a national random sample of 654 such women. We assumed there that the population standard deviation was known to be σ = 7.5.
Read carefully. You read in the report of a psychology experiment: “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,
Because the t procedures are robust, the most important condition for their safe use is that(a) the population standard deviation σ is known.(b) the population distribution is exactly Normal.(c) the data can be regarded as an SRS from the population
Which of these settings does not allow use of a matched pairs t procedure?(a) You interview both the husband and the wife in 64 married couples and ask each about their ideal number of children.(b) You interview a sample of 64 unmarried male students and another sample of 64 unmarried female
Which of the following would cause the most worry about the validity of the confidence interval you calculated in the previous exercise?(a) There is a clear outlier in the data.(b) A stemplot of the data shows a mild right skew.(c) You do not know the population standard deviation σ.
Data on the blood cholesterol levels of 24 rats (milligrams per deciliter of blood)give x = 85 and s = 12. A 95% confidence interval for the mean blood cholesterol of rats under this condition is(a) 79.9 to 90.1. (b) 80.2 to 89.8. (c) 84.0 to 86.0.
You are testing H0: μ = 0 against Ha: μ = 0 based on an SRS of 15 observations from a Normal population. What values of the t statistic are statistically significant at the α = 0.005 level?(a) t < −3.326 or t > 3.326 (b) t < −3.286 or t > 3.286 (c) t > 2.977
You have an SRS of 15 observations from a Normally distributed population. What critical value would you use to obtain a 98% confidence interval for the mean μ of the population?(a) 2.326 (b) 2.602 (c) 2.624
The P-value for the statistic in the previous exercise(a) falls between 0.01 and 0.02.(b) falls between 0.02 and 0.04.(c) is greater than 0.25.
You are testing H0: μ = 10 against Ha: μ < 10 based on an SRS of 20 observations from a Normal population. The t statistic is t = −2.25. The degrees of freedom for this statistic are(a) 19. (b) 20. (c) 21.
You are testing H0: μ = 10 against Ha: μ < 10 based on an SRS of 20 observations from a Normal population. The data give x = 8 and s = 4. The value of the t statistic is(a) −0.5. (b) −10. (c) −2.24.
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.(b) z requires that you know the population standard deviation σ.(c) z requires that you can regard your data as an SRS from the population.
Two types of error. Go to the Statistical Significance applet. This applet carries out•••APPLET tests at a fixed significance level. When you arrive, the applet is set for the colatasting test of Example 15.7. That is, the hypotheses are H0: μ = 0 Ha: μ > 0 We have an SRS of size 10 from a
Find the error probabilities. You have an SRS of size n = 9 from a Normal distribution with σ = 1. You wish to test H0: μ = 0 Ha: μ > 0 You decide to reject H0 if x > 0 and to accept H0 otherwise.(a) Find the probability of a Type I error. That is, find the probability that the test rejects H0
Power. You read that a statistical test at the α = 0.01 level has probability 0.14 of making a Type II error when a specific alternative is true. What is the power of the test against this alternative?
Error probabilities. You read that a statistical test at significance level α = 0.05 has power 0.78. What are the probabilities of Type I and Type II errors for this test?
Finding power by hand: two-sided test. The previous exercise shows how to calculate the power of a one-sided z test. Power calculations for two-sided tests follow the same outline.We will find the power of a test based on 6 measurements of the conductivity of a liquid, reported in Exercise 15.13.
Finding power by hand. Even though software is used in practice to calculate power, doing the work by hand builds your understanding. Return to the test in Example 15.7. There are n = 10 observations from a population with standard deviationσ = 1 and unknown mean μ. We will test H0: μ = 0 Ha: μ
Power. In Exercise 15.41, a sample from a Normal population with mean μ = 10 APPLET ••• and standard deviation σ = 2 failed to reject the null hypothesis H0: μ = 8 at theα = 0.05 significance level. Enter the information from this example into the Power of a Test applet. (Don’t forget
Treating knee pain. An article in the New England Journal of Medicine describes a double-blind randomized clinical trial that compared a type of surgery for knee pain due to arthritis with a placebo surgery. The experiment found no significant difference between the treatment and the placebo.
How valium works. Valium is a common antidepressant and sedative. A study investigated how valium works by comparing its effect on sleep in 7 genetically modified mice and 8 normal control mice. There was no significant difference between the two groups. The authors say that this lack of
The first child has higher IQ. Does the birth order of a family’s children influence their IQ scores? A careful study of 241,310 Norwegian 18- and 19-year-olds found that firstborn children scored 2.3 points higher on the average than second children in the same family. This difference was highly
How far do rich parents take us? How much education children get is strongly associated with the wealth and social status of their parents. In social science jargon, this is “socioeconomic status,”or SES. But the SES of parents has little influence on whether children who have graduated from
Helping welfare mothers. A study compares two groups of mothers with young children who were on welfare two years ago. One group attended a voluntary training program that was offered free of charge at a local vocational school and was advertised in the local news media. The other group did not
A test goes wrong. Software can generate samples from (almost) exactly Normal distributions. Here is a random sample of size 5 from the Normal distribution with mean 10 and standard deviation 2:6.47 7.51 10.10 13.63 9.91 These data match the conditions for a z test better than real data will: the
Predicting success of trainees. What distinguishes managerial trainees who eventually become executives from those who don’t succeed and leave the company?We have abundant data on past trainees—data on their personalities and goals, their college preparation and performance, even their family
Why are larger samples better? Statisticians prefer large samples. Describe briefly the effect of increasing the size of a sample (or the number of subjects in an experiment) on each of the following:(a) The margin of error of a 95% confidence interval.(b) The P-value of a test, when H0 is false
What is significance good for? Which of the following questions does a test of significance answer? Briefly explain your replies.(a) Is the sample or experiment properly designed?(b) Is the observed effect due to chance?(c) Is the observed effect important?
When to use pacemakers. A medical panel prepared guidelines for when cardiac pacemakers should be implanted in patients with heart problems. The panel reviewed a large number of medical studies to judge the strength of the evidence supporting each recommendation. For each recommendation, they
Can we trust this interval? Here are data on the percent change in the total mass (in tons) of wildlife in severalWest African game preserves in the years 1971 to 1999:8 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 2.9 3.1 −1.2 −1.1 −3.3 3.7 1.9 −0.3 −5.9 −7.9 1981 1982 1983 1984
An outlier strikes. You have data on an SRS of recent graduates from your college that shows how long each student took to complete a bachelor’s degree. The data contain one high outlier. Will this outlier have a greater effect on a confidence interval for mean completion time if your sample is
College degrees. At the Census Bureau Web site www.census.gov you can find the percent of adults in each state who have at least a bachelor’s degree. It makes no sense to find x for these data and use it to get a confidence interval for the mean percent μ in all 50 states. Why not?
Sensitive questions. The National AIDS Behavioral Surveys found that 170 individuals in its random sample of 2673 adult heterosexuals said they had multiple sexual partners in the past year. That’s 6.36% of the sample. Why is this estimate likely to be biased? Does the margin of error of a 95%
Pulling wood apart. You want to estimate the mean load needed to pull apart the pieces of wood in Exercise 14.50 (page 389) to within ±1000 pounds with 95%confidence. How large a sample is needed?
Sampling at the mall. A market researcher chooses at random from women entering a large suburban shopping mall. One outcome of the study is a 95% confidence interval for the mean of “the highest price you would pay for a pair of casual shoes.”(a) Explain why this confidence interval does not
Hotel managers. In Exercise 14.42 (page 387) you carried out a test of significance based on the BSRI femininity scores of 148 male general managers of three-star and four-star hotels. You now realize that a confidence interval for the mean score of male hotel managers would be more informative
Color blindness in Africa. An anthropologist claims that color blindness is less common in societies that live by hunting and gathering than in settled agricultural societies. He tests a number of adults in two populations in Africa, one of each type. The proportion of color-blind people is
Hotel managers. In Exercise 14.42 (page 387) you carried out a test of significance based on data from 148 general managers of three-star and four-star hotels. Before you trust your results, you would like more information about the data. What facts would you most like to know?
(Optional) The power of a test is important in practice because power(a) describes how well the test performs when the null hypothesis is actually true.(b) describes how sensitive the test is to violations of conditions such as Normal population distribution.(c) describes how well the test performs
(Optional) The power of the test in the previous exercise against the specific alternativeμ = 3 is defined as(a) the probability that the test rejects H0 when μ = 1 is true.(b) the probability that the test rejects H0 when μ = 3 is true.(c) the probability that the test fails to reject H0 when
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 μ = 1. An increase to μ = 3
A laboratory scale is known to have a standard deviation of σ = 0.001 gram in repeated weighings. Scale readings in repeated weighings are Normally distributed, with mean equal to the true weight of the specimen. How many times must you weigh a specimen on this scale in order to get a margin of
Vigorous exercise helps people live several years longer (on the average). Whether mild activities like slow walking extend life is not clear. Suppose that the added life expectancy from regular slow walking is just 2 months. A statistical test is more likely to find a significant increase in mean
A writer in a medical journal says: “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 writer is skeptical about the significant improvement
Many sample surveys use well-designed random samples but half or more of the original sample can’t be contacted or refuse to take part. Any errors due to this nonresponse(a) have no effect on the accuracy of confidence intervals.(b) are included in the announced margin of error.(c) are in
You turn your Web browser to the online Harris Interactive poll. Based on 6748 responses, the poll reports that 16% of U.S. adults sometimes use the Internet to make telephone calls.7 You should refuse to calculate a 95% confidence interval based on this sample because(a) the poll was taken a week
The coach of a college men’s basketball team records the resting heart rates of the 15 team members. You should not trust a confidence interval for the mean resting heart rate of all male students at this college based on these data because(a) with only 15 observations, the margin of error will
The most important condition for sound conclusions from statistical inference is usually(a) that the data can be thought of as a random sample from the population of interest.(b) that the population distribution is exactly Normal.(c) that the data contain no outliers.
How many females were among the respondents?(a) 2625(b) 4877(c) Need more information
How many individuals are described by this table?(a) 2625(b) 4877(c) Need more information
Tests from confidence intervals. A 95% confidence interval for a population mean is 31.5 ± 3.4. Use the method described in the previous exercise to answer these questions.(a) With a two-sided alternative, can you reject the null hypothesis that μ = 34 at the 5% (α = 0.05) significance level?
Tests from confidence intervals. A confidence interval for the population meanμ tells us which values of μ are plausible (those inside the interval) and which values are not plausible (those outside the interval) at the chosen level of confidence.You can use this idea to carry out a test of any
This wine stinks. Are untrained students less sensitive on the average than trained tasters in detecting “off-odors” in wine? Exercise 14.54 gives the lowest levels of dimethyl sulfide (DMS) that 10 students could detect. The units are micrograms of DMS per liter of wine (μg/l). Assume that
Eye grease. Athletes performing in bright sunlight often smear black eye grease under their eyes to reduce glare. Does eye grease work? In one study, 16 student subjects took a test of sensitivity to contrast after 3 hours facing into bright sun, both with and without eye grease. This is a matched
This wine stinks. Sulfur compounds cause “off-odors”in wine, so winemakers want to know the odor threshold, the lowest concentration of a compound that the human nose can detect. The odor threshold for dimethyl sulfide (DMS) in trained wine tasters is about 25 micrograms per liter of wine
Bone loss by nursing mothers. Exercise 14.51 gives the percent change in the mineral content of the spine for 47 mothers during three months of nursing a baby.As in that exercise, suppose that the percent change in the population of all nursing mothers has a Normal distribution with standard
Pulling wood apart. Exercise 14.50 gives data on the pounds of load needed to pull apart pieces of Douglas fir. The data are a random sample from a Normal distribution with standard deviation 3000 pounds.(a) Is there significant evidence at the α = 0.10 level against the hypothesis that the mean
Bone loss by nursing mothers. Breast-feeding mothers secrete calcium into their milk. Some of the calcium may come from their bones, so mothers may lose bone mineral. Researchers measured the percent change in mineral content of the spines of 47 mothers during three months of breast-feeding.13 Here
Pulling wood apart. How heavy a load (pounds) is needed to pull apart pieces of Douglas fir 4 inches long and 1.5 inches square? Here are data from students doing a laboratory exercise:33,190 31,860 32,590 26,520 33,280 32,320 33,020 32,030 30,460 32,700 23,040 30,930 32,720 33,650 32,340 24,050
The wrong P. The report of a study of seat belt use by drivers says, “Hispanic drivers were not significantly more likely than White/non-Hispanic drivers to overreport safety belt use (27.4 vs. 21.1%, respectively; z = 1.33, P > 1.0.)”12 How do you know that the P-value given is incorrect? What
The wrong alternative. One of your friends is comparing movie ratings by female and male students for a class project. She starts with no expectations as to which sex will rate a movie more highly. After seeing that women rate a particular movie more highly than men, she tests a one-sided
5% versus 1%. Sketch the standard Normal curve for the z test statistic and mark off areas under the curve to show why a value of z that is significant at the 1% level in a one-sided test is always significant at the 5% level. If z is significant at the 5%level, what can you say about its
Forests and windstorms. Does the destruction of large trees in a windstorm change forests in any important way? Here is the conclusion of a study that found that the answer is “No”:We found surprisingly little divergence between treefall areas and adjacent control areas in the richness of woody
Cicadas as fertilizer? Every 17 years, swarms of cicadas emerge from the ground in the eastern United States, live for about six weeks, then die. There are so many cicadas that their dead bodies can serve as fertilizer. In an experiment, a researcher added cicadas under some plants in a natural
How to show that you are rich. Every society has its own marks of wealth and prestige. In ancient China, it appears that owning pigs was such a mark. Evidence comes from examining burial sites. The skulls of sacrificed pigs tend to appear along with expensive ornaments, which suggests that the
Is this what P means? When asked to explain the meaning of “the P-value was P = 0.03,” a student says, “This means there is only probability 0.03 that the null hypothesis is true.”Explain what P = 0.03 really means in a way that makes it clear that the student’s explanation is wrong.
Hotel managers’ personalities. Successful hotel managers must have personality characteristics often thought of as feminine (such as “compassionate”) as well as those often thought of as masculine (such as “forceful”). The Bem Sex-Role Inventory(BSRI) is a personality test that gives
I want more muscle. If young men thought that their own level of muscle was about what women prefer, the mean “muscle gap”in the study described in Exercise 14.35 would be 0.We suspect (before seeing the data) that young men think women prefer more muscle than they themselves have.(a) State
Student study times. Exercise 14.34 describes a class survey in which students claimed to study an average of x = 137 minutes on a typical weeknight. Regard these students as an SRS from the population of all first-year students at this university.Does the study give good evidence that students
Explaining confidence. Here is an explanation from the Associated Press concerning one of its opinion polls. Explain briefly but clearly in what way this explanation is incorrect.For a poll of 1,600 adults, the variation due to sampling error is no more than three percentage points either way. The
Explaining confidence. You ask another student to explain the confidence interval for mean BMI described in the previous exercise. The student answers,“We can be 95% confident that future samples of young women will have mean BMI between 26.2 and 27.4.” Is this explanation correct? Explain your
Explaining confidence. A student reads that a 95% confidence interval for the mean body mass index (BMI) of young American women is 26.8 ± 0.6. Asked to explain the meaning of this interval, the student says, “95% of all young women have BMI between 26.2 and 27.4.” Is the student right?
An outlier strikes. There were actually 270 responses to the class survey in Exercise 14.34. One student claimed to study 30,000 minutes per night. We know he’s joking, so we left out this value. If we did a calculation without looking at the data, we would get x = 248 minutes for all 270
I want more muscle. Young men in North America and Europe (but not in Asia)tend to think they need more muscle to be attractive. One study presented 200 young American men with 100 images of men with various levels of muscle.7 Researchers measure level of muscle in kilograms per square meter
Student study times. A class survey in a large class for first-year college students asked, “About how many minutes do you study on a typical weeknight?”The mean response of the 269 students was x = 137 minutes. Suppose that we know that the study time follows a Normal distribution with
You use software to carry out a test of significance. The program tells you that the P-value is P = 0.031. This means that(a) the probability that the null hypothesis is true is 0.031.(b) the value of the test statistic is 0.031.(c) a test statistic as extreme as these data give would happen with
The alternative hypothesis for the test in Exercise 14.31 is(a) Ha: μ = 18. (b) Ha: μ < 18. (c) Ha: μ = 16.5.
Experiments on learning in animals sometimes measure how long it takes mice to find their way through a maze. The mean time is 18 seconds for one particular maze. A researcher thinks that a loud noise will cause the mice to complete the maze faster. She measures how long each of 10 mice takes with
Another specimen is weighed 8 times on this scale. The average weight is 4.1602 grams. A 99% confidence interval for the true weight of this specimen is(a) 4.1602 ± 0.00032. (b) 4.1602 ± 0.00069. (c) 4.1602 ± 0.00091.
The z statistic for testing H0: μ = 3.41 based on these 3 measurements is(a) z = 0.004. (b) z = 4. (c) z = 6.928.
You want a 99% confidence interval for the true weight of this specimen. The margin of error for this interval will be(a) smaller than the margin of error for 95% confidence.(b) greater than the margin of error for 95% confidence.(c) about the same as the margin of error for 95% confidence.
A 95% confidence interval for the true weight of this specimen is(a) 3.414 ± 0.00113. (b) 3.414 ± 0.00065. (c) 3.414 ± 0.00196.
The z statistic for a one-sided test is z = 2.433. This test is(a) not significant at either α = 0.05 or α = 0.01.(b) significant at α = 0.05 but not at α = 0.01.(c) significant at both α = 0.05 and α = 0.01.Use the following information for Exercises 14.27 through 14.30. A laboratory scale
You use software to carry out a test of significance. The program tells you that the P-value is P = 0.031. This result is(a) not significant at either α = 0.05 or α = 0.01.(b) significant at α = 0.05 but not at α = 0.01.(c) significant at both α = 0.05 and α = 0.01.
To give a 96% confidence interval for a population mean μ, you would use the critical value(a) z∗ = 1.960. (b) z∗ = 2.054. (c) z∗ = 2.326.
The continuity correction. One reason why the Normal approximation may fail to give accurate estimates of binomial probabilities is that the binomial distributions are discrete and the Normal distributions are continuous. That is, counts take only whole number values but Normal variables can take

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