# Stream quality is based on the levels of many variables

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1. Stream quality is based on the levels of many variables, including the following. Which of these variables is quantitative?

The amount of dissolved oxygen

The number of distinct species present

The amount of phosphorus

All of the above

2. Which of the following is a discrete variable?

Weight of a fish

Length of a fish

None of the above

Number of toxins present in a fish

3. During winter, red foxes hunt small rodents by jumping into thick snow cover. Researchers report that a hunting trip lasts on average 19 minutes and involves on average 7 jumps. They also report that, surprisingly, 79% of all successful jumps are made in the northeast direction. Three variables are mentioned in this report. The first variable mentioned is

ordinal.

quantitative and discrete.

quantitative and continuous.

categorical.

4. A sample of 55 streams in severe distress was obtained during 2007. The following is a bar graph of the number of streams that are from the Northeast, Northwest, Southeast, or Southwest. In the bar graph, the bar for the Northeast has been omitted.

The number of streams from the Northeast is

35.

25.

15.

45.

5. Here is a stemplot (with split stems) of body temperatures (in degrees Fahrenheit) for 65 healthy adult women.

The first quartile for this data set is

97.6.

97.5.

98.0.

97.9.

6. Researchers measured the length of the central retrix (R1), a flight-involved tail feather, in 21 female long-tailed finches. Here is a boxplot of the length, in millimeters (mm).

Based on this boxplot, which of the following statements is TRUE?

The distribution of R1 lengths is bimodal.

The distribution of R1 lengths is mildly right-skewed with a high outlier.

75% of the birds in this study had an R1 length above 70 mm.

All of the above

7. Geckos are lizards with specialized toe pads that enable them to easily climb all sorts of surfaces. A research team examined the adhesive properties of 7 Tokay geckos. Below are their toe-pad areas (in square centimeters, cm2).

5.6 4.9 6.0 5.1 5.5 5.1 7.5

To be an outlier, an observation must fall outside the range

4.9 to 7.5.

4.2 to 6.9.

3.75 to 7.35.

5.1 to 6.0.

8. The median age of five people on a committee is 30 years. One of the members, whose age is 50 years, resigns. The median age of the remaining four people in the committee is

not able to be determined from the information given.

25 years.

30 years.

40 years.

9. By inspection, determine which of the following sets of numbers has the smallest standard deviation.

7, 8, 9, 10

0, 0, 10, 10

0, 1, 2, 3

5, 5, 5, 5

10. The volume of oxygen consumed (in liters per minute) while a person is at rest and while he or she is exercising (running on a treadmill) was measured for each of 50 subjects. The goal is to determine if the volume of oxygen consumed during aerobic exercise can be estimated from the amount consumed at rest. The results are plotted below.

The scatterplot suggests that

there is a positive association between the volume of oxygen consumed at rest and while running.

there is an outlier in the plot.

both 1 and 2 are true.

neither 1 nor 2 is true.

11. Bird species from temperate regions must cope with relatively short breeding seasons. A study examined the relationship between blood testosterone level (ng/ml) and the duration of the egg-laying period (months) in temperate bird species. The scatterplot below displays this relationship, after taking the logarithm of each variable.

A plausible value for the correlation between the logarithm of egg-laying duration and the logarithm of testosterone level is

–0.9.

–0.4.

+0.2.

+0.8.

12. When water flows across farm land, some of the soil is washed away, resulting in erosion. An experiment was conducted to investigate the effect of the rate of water flow (in liters per second) on the amount of soil washed away (in kilograms). The data are given in the following table.

Flow rate 0.31 0.85 1.26 2.47 3.75

Eroded soil 0.82 1.95 2.18 3.01 6.07

The association between flow rate and amount of eroded soil is

neither positive nor negative.

positive.

impossible to determine since both variables are categorical.

negative.

13. Which of the following is TRUE of the correlation coefficient r?

If r is the correlation between X and Y, then –r is the correlation between Y and X.

All of the above

–1 r 1.

It is a resistant measure of association.

14. Researchers want to know if reading skills can explain IQ test scores in children with dyslexia. The following scatterplot examines the relationship between reading skill score and IQ test score for 22 dyslexic children. The least-squares regression line is displayed on the plot, along with the value of r2.

The intercept of the least-squares regression line

cannot be determined from the graph, even approximately.

is greater than 120.

is less than 50.

is about 80, approximately.

15. Researchers want to know if reading skills can explain IQ test scores in children with dyslexia. The following scatterplot examines the relationship between reading skill score and IQ test score for 22 dyslexic children. The least-squares regression line is displayed on the plot, along with the value of r2.

What percent of the variation in IQ test scores is explained by this regression model?

5%

48%

23%

52%

16. Before surgical removal of a diseased parathyroid gland, two tests are often performed: the standard intact test and the turbo test. Both tests measure parathyroid hormone (PTH, in ng/l), but the turbo test is very expensive. Researchers obtained data from both tests in a sample of 48 patients to predict turbo test results (y) from standard intact test results (x). The data ranged from roughly 0 to 500 ng/l, and a scatterplot showed a clear linear relationship. The published findings are summarized exactly as follows:

y = 1.08x – 4.36 (r = 0.97; n = 48)

For a PTH level of x = 1000 ng/l with the standard intact test, the predicted PTH level with the turbo test

is 1075.64 ng/l.

is 1036.4 ng/l.

cannot be predicted accurately because it would be extrapolating.

is 970 ng/l.

17. Babies typically learn to crawl approximately six months after birth. However, it may take longer for babies to learn to crawl in the winter, when they are often bundled in clothes that restrict their movement. Thus, there may be an association between a baby’s crawling age and the average temperature during the month they first try to crawl. Below are the average ages (in weeks) at which babies began to crawl for a sample of babies born in each of the 12 months of the year. In addition, the average temperature (in °F) for the month that is six months after the birth month is also listed.

Birth month Average crawling age Average temperature

January 29.84 66

February 30.52 73

March 29.70 72

April 31.84 63

May 28.58 52

June 31.44 39

July 33.64 33

August 32.82 30

September 33.83 33

October 33.35 37

November 33.38 48

December 32.32 57

We want to investigate if the average age at which infants begin to crawl (y) can be predicted from the average outdoor temperature (x) six months after birth, when they are likely to begin crawling. We decide to fit a least-squares regression line to the data with x as the explanatory variable and y as the response variable. We compute the following quantities.

r = correlation between x and y = –0.7

= mean of the values of x = 50.25

= mean of the values of y = 31.77

sx = standard deviation of the values of x = 15.85

sy = standard deviation of the values of y = 1.76

Which of the following is closest to the slope of the least-squares line?

0.08

–0.08

6.30

–6.30

18. Babies typically learn to crawl approximately six months after birth. However, it may take longer for babies to learn to crawl in the winter, when they are often bundled in clothes that restrict their movement. Thus, there may be an association between a baby’s crawling age and the average temperature during the month they first try to crawl. Below are the average ages (in weeks) at which babies began to crawl for a sample of babies born in each of the 12 months of the year. In addition, the average temperature (in °F) for the month that is six months after the birth month is also listed.

Birth month Average crawling age Average temperature

January 29.84 66

February 30.52 73

March 29.70 72

April 31.84 63

May 28.58 52

June 31.44 39

July 33.64 33

August 32.82 30

September 33.83 33

October 33.35 37

November 33.38 48

December 32.32 57

We want to investigate if the average age at which infants begin to crawl (y) can be predicted from the average outdoor temperature (x) six months after birth, when they are likely to begin crawling. We decide to fit a least-squares regression line to the data with x as the explanatory variable and y as the response variable. We compute the following quantities.

r = correlation between x and y = –0.7

= mean of the values of x = 50.25

= mean of the values of y = 31.77

sx = standard deviation of the values of x = 15.85

sy = standard deviation of the values of y = 1.76

The fraction of the variation in the values of a response y that is explained by the least-squares regression of y on x is the

intercept of the least-squares regression line.

correlation coefficient.

square of the correlation coefficient.

slope of the least-squares regression line.

19. The city council in a suburb of Raleigh is interested in the level of public support for a tax increase to support restoration of nearby parks and waterways. A marketing research firm is selected that then selects a simple random sample of 50 adult residents and contacts each to determine whether the resident would be opposed to the tax increase. Of these, 15 indicated that they would be opposed.

The population of interest is

all adult residents in the suburb.

the residents in the suburb that are opposed to the tax increase.

the 50 residents contacted.

all households in the suburb.

20. The National Health and Nutrition Examination Survey (NHANES) assesses the health and nutritional status of Americans. A recent NHANES asked a random sample of 17,567 American adults to fill a detailed questionnaire about what they ate the previous day and give their body mass index (BMI). The researchers then compared individuals who ate avocado with those who didn’t, and found that BMI was lower, on average, among those who ate avocado. This is an example of

a survey using a probability sample.

a retrospective case-control study.

just anecdotal evidence.

a prospective cohort.

21. You need to select three subjects from a list of nine subjects. The subjects’ names are provided below.

1. Berliner 4. Wolfe 7. Verducci

2. Blumenthal 5. Stasny 8. Lin

3. MacEachern 6. Santner 9. Critchlow

Use the numerical labels attached to the names and the following list of random digits to select three individuals. Read the list of random digits from left to right, starting at the beginning of the list.

44982 20751 27498 12009 45287 71753 98236 66419 84533 11793 20495 05907 11384

Which of the following statements is TRUE?

If we used another list of random digits to select the sample, the result obtained with the list actually used would be just as likely to be selected as any other set of three names.

If we used another list of random digits to select the sample, we would get a completely different sample than that obtained with the list actually used.

If we used another list of random digits to select the sample, we would get at most one name in common with a name obtained with the list actually used.

If we used another list of random digits to select the sample, we would get the same result as obtained with the list actually used.

22. Sixty-four pregnant women ranked the severity of their heartburn during pregnancy. Researchers rated newborn hair volume using photographs of the newborn’s head. They found an association between heartburn severity during pregnancy and the amount of hair on newborns. What can we reasonably conclude from this study?

Pregnancy is confounded with heartburns in deciding the cause of newborn hair amount.

Newborn hair causes heartburns in pregnant women.

Eating food causing heartburns during pregnancy leads to newborns that are hairier.

A lurking variable likely influences both the severity of heartburns in pregnant women and the amount of hair on newborns.

23. A March 2010 SurveyUSA telephone poll asked about issues facing central Ohio to a random sample of 500 households in the Columbus, Ohio, area. One question was: “Where 10 means most important, and 1 means least important, how important is protecting the environment?” The average response was 6.0.

What population is the poll targeting?

The poll targets the 500 households in the Columbus area who responded.

The poll targets all households with a strong opinion on the environment in the Columbus area.

The poll targets registered voters in the Columbus area.

The poll targets all households in the Columbus area.

24. A researcher is interested in investigating the relationship between sugar consumption and weight gain for high school students. Fifteen volunteers were randomly assigned to one of two groups. The first group contained six volunteers who were put on a low-sugar diet. The second group consisting of the remaining nine volunteers was put on a diet with sugar constituting approximately 15% of their diet. After eight weeks, the change in weight was recorded for each of the volunteers.

The response is the

eight-week time period.

assignment to groups.

percent of sugar in the diet.

change in weight.

25. A researcher was studying how the weights of horseshoe crabs along the east coast varied between northern and southern habitats. In spring 2006, during breeding season, the researcher randomly selected 50 horseshoe crabs in southern habitats. In fall 2006, before breeding season begins, the researcher randomly selected 50 horseshoe crabs from northern habitats. It was found that crabs in southern habitats weighed more and so the researcher claimed that location had an effect on weight of horseshoe crabs. The results cannot be trusted because the

investigator should have used more than two locations.

investigator was biased. She knew beforehand what the study would show.

time of year during which the samples were taken is a confounding variable.

study was not double-blind.

26. Researchers wish to determine if a new experimental medication will reduce the symptoms of allergy sufferers without the side effect of drowsiness. To investigate this question, the researchers give the new medication to 50 adult volunteers who suffer from allergies. Forty-four of these volunteers report a significant reduction in their allergy symptoms without any drowsiness.

This study could be improved by

including people who do not suffer from allergies in the study in order to represent a more diverse population.

repeating the study using only the volunteers who reported a significant reduction in their allergy symptoms without any drowsiness and giving them a higher dosage this time.

using a control group.

All of the above

27. Will a fluoride mouthwash used after brushing reduce cavities? Twenty sets of twins were used to investigate this question. One member of each set of twins used the mouthwash after each brushing, the other did not. After six months, the difference in the number of cavities of those using the mouthwash was compared with the number of those who did not use the mouthwash. This experiment uses

double replication.

a matched pairs design.

double-blinding.

random placeboes.

28. A study examined the effect of garlic on blood cholesterol levels. A total of 192 subjects with starting LDL (“bad cholesterol”) levels between 130 and 190 mg/dl were randomly assigned to one of four treatments for six months: raw garlic eaten daily, a powdered garlic supplement taken daily (Garlicin brand), an aged-garlic extract taken daily (Kyolic brand), or a placebo pill taken daily. The study found no significant or clinical differences in blood cholesterol levels between the four groups at the end of the study.

This study uses the principles of

randomization.

blinding.

blocking.

All of the above

29. A population has an equal proportion of males and females. That is, when randomly selecting one individual, the probability that the individual is male (M) is 1/2 and the probability that the individual is female (F) is 1/2.

In the first 50 randomly selected individuals, 20 were male. In the next 50 randomly selected individuals, which of the following must happen?

More than half of the individuals will be males to balance out the low number of males in the first 50 individuals. However, the order in which these males will be selected is unpredictable.

More than 20 of the individuals will be males because the proportion of males after 100 individuals must be closer to 1/2 than the proportion after 50 individuals.

The number of males will be very close to 30 in the next 50 individuals because the proportion must be close to 1/2 after 100 individuals.

None of the above

30. The Centers for Disease Control and Prevention receives information about the causes for HIV/AIDS infection in the United States. Here are the causes of infection and their respective probability among American women ages 20 to 24 years old.

Cause Probability

Injection drug use ?

Heterosexual sex 0.664

Perinatal infection 0.125

Other causes 0.095

The probability that an American woman age 20 to 24 contracted HIV/AIDS either via heterosexual sex or via perinatal infection is

0.789.

0.211.

0.500.

0.083.

31. Based on a recent Gallup survey, we define the following probability model for the number X of daily cups of coffee consumed by Americans.

X 0 1 2 3 4 or more

Probability 0.36 0.26 0.19 0.09 ?

The probability that an American does not consume 2 cups of coffee daily is _______ .

32. A variable whose value is a numerical outcome of a random phenomenon is called

a random variable.

biased.

a random sample.

a parameter.

33. The frequency of color blindness (dyschromatopsia) in the Caucasian American male population is estimated to be about 8%. Let’s call X the number of color-blind individuals in a random sample of 8 Caucasian American males. The table below gives the probability distribution for X.

X 0 1 2 3 4 5 6 7 8

P(X) 0.513 0.357 0.109 0.019 0.002 0.000 0.000 0.000 0.000

What is the probability of getting 1 or 2 color-blind individuals in the sample?

0.248

0.870

0.466

0.039

34. Using the standard Normal distribution tables, the area under the standard Normal curve corresponding to Z > –2.62 is

0.0047.

0.9956.

0.0044.

0.9953.

35. The pH measurements of water specimens from various locations along a given river basin are Normally distributed with mean 8 and standard deviation 0.3.

What is, approximately, the probability that the pH measurement of a randomly selected water specimen is greater than 8.2?

0.2525

0.7475

0.7525

0.2475

36. A researcher is interested in the lengths of Salvelinus fontinalis (brook trout), which are known to be approximately Normally distributed with mean 80 centimeters and standard deviation 5 centimeters. To help preserve brook trout populations, some regulatory standards need to be set limiting the size of fish that can be caught. The probability of catching a brook trout less than 72 centimeters in length is

0.3745.

0.9452

0.0548.

0.6255.

37. A researcher is interested in the lengths of Salvelinus fontinalis (brook trout), which are known to be approximately Normally distributed with mean 80 centimeters and standard deviation 5 centimeters. To help preserve brook trout populations, some regulatory standards need to be set limiting the size of fish that can be caught. To ensure that the shortest 8% of the brook trout get thrown back, the lower cut-off should be set at

75.00 centimeters.

87.03 centimeters.

72.95 centimeters.

80.00 centimeters.

38. The distribution of total body protein in adult men with liver cirrhosis is approximately Normal with mean 9.8 kg and standard deviation 0.1 kg.

Twenty-five percent of adult men with cirrhosis have a total body protein of at least

9.87 kg.

9.73 kg.

9.70 kg.

9.60 kg.

39. The amount of cholesterol in a person’s body produced by their liver and other cells is proposed to be Normally distributed with mean 75% and standard deviation 0.5%.

The probability that a person produces more than 76.7% of the cholesterol in their body is

0.9997.

1.

0.0006.

0.0003.

40. A national survey by Gallup interviewed 1014 adults and found that they had consumed on average 4.2 alcoholic beverages in the past seven days.

Considering a sample of 1014 adults a large sample, which of the following is TRUE?

By the central limit theorem, the 1014 weekly number of drinks obtained in the sample are approximately Normally distributed.

By the law of large numbers, the results of this study are 1014 times less variable than if only one American adult had been asked.

By the law of large numbers, the average weekly number of drinks from repeated samples of size 1014 is approximately Normally distributed.

By the central limit theorem, the average weekly number of drinks from repeated samples of size 1014 is approximately Normally distributed.

41. The fact that the sample mean doesn’t tend to over- or under-estimate the population mean makes the sample mean

consistent.

a statistic.

unbiased.

efficient.

42. You plan to randomly select 10 students from your campus and ask them how many minutes they exercised in the past seven days.

The distribution of values taken by the average exercising time in all possible samples of size 10 is the

variance of the exercising time values.

probability distribution of exercising times.

population parameter.

sampling distribution of average exercising times.

43. The variability of a statistic is described by the

spread of its sampling distribution.

vagueness in the wording of the question used to collect the sample data.

amount of bias present.

stability of the population it describes.

44. The pH measurements of water specimens from various locations along a given river basin are Normally distributed with mean 8 and standard deviation 0.3. You take water specimens from 4 randomly selected locations on this river basin.

Use the 68–95–99.7 rule to answer this question. What is the range of average pH measurements that make up roughly the middle 95% of the sampling distribution for random samples of 4 specimens?

7.7 to 8.3

7.4 to 8.6

7.85 to 8.15

7.925 to 8.075

45. The distribution of total body protein in adult men with liver cirrhosis is approximately Normal with mean 9.8 kg and standard deviation 0.1 kg.

If you take a random sample of 25 adult men with liver cirrhosis, what is the probability that their average total body protein is between 9.75 and 9.85 kg?

0.3829

0.0796

0.0062

0.9876

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