ANIMSCI 2600, Midterm 1

Measures of variation include

range, variance, and standard deviation

If we roll a single die, the sample points are 1, 2, 3, 4, 5, or 6. Consider the following two events: Event A: toss an even number on the die Event B: toss a number less than or equal to 3 on the die List the sample points that would be included in the union of events A and B (i.e., A U B).

{1, 2, 3, 4, 6}

If we roll a single die, the sample points are 1, 2, 3, 4, 5, or 6. Consider the following two events: Event A: toss an even number on the die Event B: toss a number less than or equal to 3 on the die List the sample points that would be included in the intersection of events A and B (i.e., A ∩ B).

{2}

If we were to construct a relative frequency bar graph for the breeds of dogs in a kennel, the heights of the bars would represent the

Proportion of dogs in each breed.

Pie charts normally show the

Proportion of observations falling in each class.

The types of trees (maple, oak, elm, etc.) in a nursery are an example of a ____________ variable.

Qualitative

____________ data are non numerical data that can only be classified into one of a group of categories.

Qualitative

The manager of a car dealership records the colors of the automobiles on his used car lot. The type of data being collected is ____________.

Qualitative data

The breeds of dogs in a kennel are an example of what type of variable?

Qualitative variable

Starting salary and GPA of students who graduate from OSU are examples of ____________ data.

Quantitative data

Sandoz, a pharmaceutical firm, reports that kidney transplant patients who receive the drug cyclosporine have an 80% chance of surviving the first year. Suppose a hospital performs 4 kidney transplants and all 4 patients receive cyclosporine. Assuming that one patient's survival is independent of another's, what is the probability that none of the 4 patients will be alive at the end of 1 year?

0.0016

Assume that the probabilities of two genetic defects (we will call them defect A and defect B) in horses are 0.10 and 0.15, respectively. If these two genetic defects represent independent events, what is the probability that a horse will have both of these genetic defects?

0.015

A consumer taste panel study was conducted to determine how people rate the eating quality of steaks from Brahman cattle. Members of the taste panel were asked to rate the overall quality of the steaks from 0 (no quality at all) to 100 (extremely good quality). The stem-and-leaf display of the data is shown below. Stem Leaves 3 2 4 4 0 3 4 7 8 9 9 9 5 0 1 1 2 3 4 5 6 1 2 5 6 6 7 0 1 8 9 2 What proportion of the taste panel members rated overall eating quality of the Brahman steaks as very good (i.e., a score of 80 or above)?

0.04

Assume that the probability that a calf will be red in color is 0.25 and the probability that the calf will have horns is 0.50. Coat color and the presence or absence of horns are independent events. What is the probability that the calf will be red and will have horns?

0.125

A statistician evaluated the winning strategies of teams in the National Football League (NFL). He used actual NFL play-by-play data to approximate the probabilities associated with certain outcomes (e.g., running plays, short pass plays, and long pass plays). The table below shows the probability distribution for the yardage gained, X, on a running play. A negative gain represents a loss of yards on the play. Find the probability of losing yardage on a running play. X, Yards Gained Probability -4 0.020 -2 0.060 -1 0.070 0 0.150 1 0.130 2 0.110 3 0.090 4 0.070 6 0.090 8 0.060 10 0.050 15 0.085 30 0.010 50 0.004 99 0.001

0.15

Suppose that 80% of the Holstein cows in the U.S. give birth to their calves with no calving difficulty. We randomly select 4 Holstein cows from the population consisting of all Holstein cows in the U.S. What is the probability that exactly 3 of the 4 cows in this sample will give birth to their calves with no calving difficulty? To find the answer to this question, you will need to use the equation for the binomial distribution.

0.512

Find the proportion of the population expected to lie within one standard deviation of the mean of a binomial probability distribution with a sample size of n = 20 and a probability of success of 0.60.

0.7468

Weights of 15 pigs are used to construct the following stem-and-leaf display: stem leaf 21 0 22 2 5 5 7 9 23 1 2 8 9 24 1 4 6 25 2 4 Using the stem-and-leaf display, find the 25th percentile.

225

Suppose that 20% of the Labrador Retrievers in the U.S. have a particular genetic defect. We randomly select 7 Labs from the population consisting of all Labs in the U.S. What is the probability that at least 1 of the 7 dogs in this sample has the genetic defect?

0.7903

An experiment results in one of two possible outcomes, A or B. We know that P(A) = 0.40, P(B) = 0.60, and P(A ∩ B) = 0.20. Find the P(A U B).

0.80

An experiment results in five possible outcomes with the following probabilities: P(A) = .10, P(B) = .25, P(C) = .20, P(D) = .15, and P(E) = .30. What is the probability that event A does not occur?

0.90

We have an event A and an event B, where P(A) = 0.80 P(B) = 0.20 P(A intersect B) = 0.10 Find P(A union B).

0.90

Finnish Landrace ewes are noted for producing "litters" of lambs. The number of lambs in a litter for a sample of 6 Finnish Landrace ewes is as follows: Ewe Number Number of Lambs in Litter 1 3 2 4 3 3 4 2 5 5 6 4 Calculate the standard deviation of litter size.

1.04881 lambs

In a pizza takeout restaurant, the following probability distribution was obtained. The random variable X represents the number of toppings for a large pizza. x 0 1 2 3 4 P(x) 0.30 0.40 0.20 0.06 0.04 Calculate the variance of this discrete probability distribution.

1.0804

In a pizza takeout restaurant, the following probability distribution was obtained. The random variable X represents the number of toppings for a large pizza. x 0 1 2 3 4 P(x) 0.30 0.40 0.20 0.06 0.04 Calculate the mean (µ) of this discrete probability distribution.

1.14

The ages (in years) of a sample of 6 students are as follows: Student Age 1 19 2 23 3 20 4 20 5 19 6 19 Calculate the standard deviation of this sample of 6 student ages.

1.5492 years

How many classes are recommended in a histogram of a data set with more than 50 observations?

15 to 20

Find the mean of a binomial probability distribution with a sample size of n = 40 and a probability of success of 0.40.

16

The ages (in years) of a sample of 6 students are as follows: Student Age 1 19 2 23 3 20 4 20 5 19 6 19 Calculate the median age of this sample of 6 students

19.5 years

Find the standard deviation of a binomial probability distribution with a sample size of n = 20 and a probability of success of 0.40.

2.19089

The weights (in pounds) of 17 pigs are used to construct the following stem-and-leaf display (the first two digits were used as the stem and the last digit was used as the leaf): Stem Leaf 16 0 5 17 -- 18 -- 19 -- 20 -- 21 -- 22 2 4 6 23 0 9 24 0 1 2 3 4 5 9 25 3 26 -- 27 -- 28 0 5 Based on this stem-and-leaf display, the median weight is __________ lb.

241

The weaning weights (in kilograms) of a sample of 6 lambs born and raised on Farmer Jones' farm are as follows: Lamb Weight 1 30 2 32 3 28 4 42 5 40 6 44 Calculate the mean weaning weight of this sample of 6 lambs.

36 kg

The weaning weights (in kilograms) of a sample of 6 lambs born and raised on Farmer Jones' farm are as follows: Lamb Weight 1 30 2 32 3 28 4 42 5 40 6 44 Find the median weaning weight of this sample of 6 lambs.

36 kg

The weights in pounds of 23 dogs were used to construct the following stem-and-leaf display using the first digit as the stem and the second digit as the leaf:. Stem Leaves 3 2 4 4 0 3 4 5 7 8 9 5 0 1 2 3 4 5 6 1 2 5 6 7 7 0 1 8 9 8 Use the stem-and-leaf display to find the lower quartile.

45 lb

An estimate that shows no consistent tendency to be above or below the true population parameter that we are trying to estimate is called

An unbiased estimate

The owner of a herd of cows wants to determine the influence of the ages of his cows on the amount of calving difficulty that occurs in his herd. He constructs the following table: Age of Cow (in years) 0-2 3-5 6-10 over 10 Total No difficulty 40 35 20 5 100 Difficult birth 35 45 15 5 100 Total 75 80 35 10 200 Find the probability that a randomly selected cow had difficulty in giving birth to her calf and was over 10 yr old.

5/200

A survey was conducted to determine how people rate the quality of programming available on TV. Twenty-one respondents were asked to rate the overall quality from 0 (no quality at all) to 100 (extremely good quality). The stem-and-leaf display based on these data (using the first digit as the stem and the second digit as the leaf) is shown below: Stem Leaves 3 2 5 4 0 3 4 7 8 9 5 1 1 2 3 4 5 6 1 2 5 6 7 7 7 8 Based on the stem-and-leaf display, the median for these TV ratings is __________.

52

The weaning weights (in kilograms) of a sample of 6 lambs born and raised on Farmer Jones' farm are as follows: Lamb Weight 1 30 2 32 3 28 4 42 5 40 6 44 Find the standard deviation of the weaning weights of this sample of 6 lambs.

6.81175 kg

The weights of 25 lambs (in pounds) in a flock of sheep are as follows: 68 73 66 76 86 74 61 89 65 90 69 92 76 62 81 63 68 81 70 73 60 87 75 64 82 Construct a stem-and-leaf display using the first digit as the stem and the second digit as the leaf. Based on the stem-and-leaf display, the lower quartile for this set of weights is __________ lb.

66 lb

According to the Empirical Rule, we expect ________ % of the observations to fall within one standard deviation of the mean, if the data have a symmetric and mound shaped distribution.

68%

The grades of 8 students on an exam were as follows: Student Grade 1 66 2 70 3 64 4 88 5 74 6 72 7 87 8 79 Find the median grade of these 8 students.

73

The weights of 25 lambs (in pounds) in a flock of sheep are as follows: 68 73 66 76 86 74 61 89 65 90 69 92 76 62 81 63 68 81 70 73 60 87 75 64 82 Construct a stem-and-leaf display using the first digit as the stem and the second digit as the leaf. Based on the stem-and-leaf display, the median for this set of weights is __________ lb.

73 lb

Health care issues are receiving a greal deal of attention in both the academic and political arenas. A sociologist recently conducted a survey of senior citizens whose net worth is too high to quality for Medicaid, but who have no private health insurance. The ages (in years) of 8 uninsured senior citizens were as follows: Senior Citizen Age 1 66 2 70 3 64 4 88 5 74 6 72 7 87 8 79 Find the median age of these 8 senior citizens.

73 years

The birth weights in pounds of 7 calves were as follows: Calf Weight 1 68 2 70 3 64 4 90 5 74 6 72 7 87 Calculate the mean birth weight of these 7 calves.

75 lb

Health care issues are receiving a greal deal of attention in both the academic and political arenas. A sociologist recently conducted a survey of senior citizens whose net worth is too high to quality for Medicaid, but who have no private health insurance. The ages (in years) of 8 uninsured senior citizens were as follows: Senior Citizen Age 1 66 2 70 3 64 4 88 5 74 6 72 7 87 8 79 Calculate the mean age of these 8 senior citizens.

75 years

The grades of 8 students on an exam were as follows: Student Grade 1 66 2 70 3 64 4 88 5 74 6 72 7 87 8 79 Find the standard deviation of the grades of these 8 students.

8.99206

The weights of 25 lambs (in pounds) in a flock of sheep are as follows: 68 73 66 76 86 74 61 89 65 90 69 92 76 62 81 63 68 81 70 73 60 87 75 64 82 Construct a stem-and-leaf display using the first digit as the stem and the second digit as the leaf. Based on the stem-and-leaf display, the upper quartile for this set of weights is __________ lb.

81 lb

The mean of the starting salary data that we have been using is 28,475 dollars and the standard deviation is 9,369 dollars. According to the Empirical Rule, we expect 95% of the starting salaries to fall between what two numbers?

9,737 and 47,213 dollars

The birth weights of 21 calves (in pounds) are as follows: 87 76 96 77 94 92 88 85 66 89 79 95 50 91 83 88 82 58 55 69 97 Construct a stem-and-leaf display using the first digit as the stem and the second digit as the leaf. Based on the stem-and-leaf display, the upper quartile for this set of birth weights is __________ lb.

91 lb

A dataset consisting of 30 observations has the following mean and standard deviation: mean = 3.74 minutesstandard deviation = 2.20 minutes What percentage of the observations would be expected to fall within the interval (-2.86, 10.34) if the data have a symmetric and mound-shaped distribution?

99%

A random sample of the weights of dogs at a local kennel yielded the following summary information: median = 80 lb lower quartile = 70 lb upper quartile = 90 lb lighest dog = 25 lb heaviest dog = 160 lb Use this information to construct a box plot and then use the box plot to determine which one of the following statements is true.

A dog that weighs 100 lb is not a suspect or highly suspect outlier, because 100 lb falls between the upper quartile of 90 lb and the upper inner fence of 120 lb.

A state energy agency mailed questionnaires on energy conservation to 1,000 homeowners in Columbus. Suppose an experiment consists of randomly selecting one of the returned questionnaires. Consider the events: Event A: the home is constructed of brick Event B: the home is more than 30 years old Event C: the home is heated with oil A home that is constructed of brick or is heated with oil would be represented by which one of the following?

A υ C

A state energy agency mailed questionnaires on energy conservation to 1,000 homeowners in Columbus. Suppose an experiment consists of randomly selecting one of the returned questionnaires. Consider the events: Event A: the home is constructed of brick Event B: the home is more than 30 years old Event C: the home is heated with oil A home that is constructed of brick and is more than 30 years old would be represented by which one of the following?

A ∩ B

The ∑ symbol in a statistical equation indicates that we are to perform which arithmetic operation?

Addition

A veterinary clinic has found that the number of patients seen per day has an average of 70 and a standard deviation of 10. If nothing is known about the shape of the distribution of number of patients seen per day, what percentage of the days would be expected to have between 50 and 90 patients?

At least 75%

Assume that the mean weight of a sample of calves is 600 lb and the standard deviation of the weights is 50 lb. If the data set does not have a symmetric and mound shaped distribution, and we therefore use Chebyshev's Rule, we would expect at least what percent of the calves to have weights between 500 and 700 lb?

At least 75%

The __________ of an event A is the event that A does not occur.

Complement

Quantitative data are

Continous

Since 1917, the Girl Scouts of America have been selling boxes of cookies. Currently, there are 12 varieties for sale. Each of the approximately 150 million boxes of Girl Scout cookies sold each year is classified by variety. The results are summarized in a pie chart. From the graph, we can clearly see that the best-selling variety is Thin Mints (25%), followed by Samoas (19%) and Tagalongs (13%). Because the figure shows the various categories of Girl Scout cookies sold, the graph is an example of ________________ statistics.

Descriptive

The American Angus Association wants to determine the proportion of their members who breed their cows using artificial insemination (AI). They randomly sample 200 of their members and ask them whether or not they breed their cows using AI. 120 of the 200 members sampled said "yes". If the American Angus Association constructed a confidence interval to estimate the true population proportion of their members who breed their cows using AI, they would be using the branch of statistics called ____________.

Inferential statistics

Which one of the following is not a measure of variation?

Mean

Given that P (A) = 0.30, P (B) = 0.60, and P (A ∩ B) = 0.15, find P (A|B).

P (A|B) = 0.25

Which of the following probabilities for the sample points A, B, and C could be true if A, B, and C are the only sample points in an experiment?

P(A) = 1/4, P(B) = 1/2, P(C) = 1/4

The for a discrete random variable (X) is a table, graph, or formula that specifies the probability of observing each value of X.

Probability distribution

The amount of television viewed by today's youth is a concern of Parents Against Watching Television (PAWT). Three-hundred parents of elementary school-aged children were asked to estimate the number of hours per week that their child watched TV. The mean and standard of their responses were 15 hours and 5 hours, respectively. Identify the type of data collected by PAWT.

Quantitative data

Weights are recorded for 500 Labrador Retriever dogs. The type of data being collected is ____________ data.

Quantitative data

Consider a study of aphasia published in the Journal of Communication Disorders. Aphasia is the "impairment or loss of the faculty of using or understanding spoken or written language." Three types of aphasia have been identified by researchers: Broca's, conduction, and anomic. The researchers wanted to determine whether one type of aphasia occurs more often than the others. Consequently, they measured the type of aphasia found in a sample of 22 adult aphasics. They found that the proportion of people with anomic, Broca's, and conduction aphasia was 0.455, 0.227, and 0.318, respectively. These proportions represent the ____________ for the three classes.

Relative frequencies

If the lower quartile is farther from the median than the upper quartile, the distribution of data is

Skewed to the left

The American Angus Association wants to determine the proportion of their members who breed their cows using artificial insemination (AI). They randomly sample 200 of their members and ask them whether or not they breed their cows using AI. 120 of the 200 members sampled said "yes". What are the experimental units?

The 200 people whose responses to the question were obtained

USA Today reported the results of a study that suggests frequently heading the ball in soccer lowers players' IQs. A psychologist tested 60 male soccer players ages 14 to 29 who played soccer up to five times per week. Players who averaged 10 or more headers per game had an average IQ of 103, whereas players who headed the ball one or fewer times per game had an average IQ of 112. The experimental units in this study are:

The 60 soccer players who participated in the study

Each year the National Opinion Research Center conducts the General Social Survey (GSS), eliciting opinions of Americans on a wide variety of social topics. One question in the survey asked about a person's belief in the Bible. A sample of 4,826 respondents selected from one of the following answers: (1) The Bible is the actual word of God, to be taken literally—1,527 respondents; (2) the Bible is the inspired word of God, but not everything is to be taken literally—2,231 respondents; (3) the Bible is an ancient book of fables, legends, history, and moral precepts—996 respondents; and (4) the Bible has some other origin—72 respondents. Find the relative frequencies for each of the 4 possible responses.

The relative frequencies are 0.3164, 0.4623, 0.2064, and 0.0149 for the Bible is the actual word of God, to be taken literally; the Bible is the inspired word of God, but not everything is to be taken literally; the Bible is an ancient book of fables, legends, history, and moral precepts; and the Bible has some other origin, respectively.

The characteristics of cheek teeth (e.g., molars) can provide anthropologists with information on the dietary habits of extinct mammals. The cheek teeth of an extinct primate species were the subject of research reported in the American Journal of Physical Anthropology (Vol. 142, 2010). A total of 18 cheek teeth extracted from skulls discovered in western Wyoming were analyzed. Each tooth was classified according to degree of wear (unknown, unworn, slight, light-moderate, moderate, moderate-heavy, or heavy). The 18 measurements were as follows: Data on Degree of Wear unknown slight unknown slight unknown heavy moderate unworn slight light-moderate unknown light-moderate moderate-heavy moderate moderate unworn slight unknown Find the relative frequency for each wear category.

The relative frequencies for the unknown, unworn, slight, light-moderate, moderate, moderate-heavy, and heavy categories are 0.2778, 0.1111, 0.2222, 0.1111, 0.1667, 0.0556, and 0.0556, respectively.

A random sample of sale prices of homes in Columbus, Ohio yielded the following summary information: Median = $125,000 Lower quartile = $82,000 Upper quartile = $168,000 Lowest price = $46,000 Highest price = $276,000 Construct a box plot for these data. Based on this box plot, is the highest selling price of $276,000 a suspect or highly suspect outlier?

The sale price of $276,000 is not a suspect or highly suspect outlier, because it falls inside the inner fences.

Assume that the mean length of time required to complete the Columbus Marathon was 4.5 hours. Further assume that the standard deviation of the times required to complete the race was 0.50 hours. One runner completed the race in 5.0 hours. Calculate the z-score for the runner with the time of 5.0 hours. Based on this z-score, is this time of 5.0 hours an outlier? Why or why not?

The time of 5.0 hours is not an outlier, because the corresponding z-score is 1.0, which is less than 3 standard deviations above the mean.

A plant scientist wants to determine the average yield (in bushels per acre) of brand X corn in Ohio. Five thousand Ohio corn fields are planted using brand X. The plant scientist is able to obtain data for the yields of 500 of these 5,000 fields. The average yield of these 500 fields planted to brand X is 175 bushels per acre. What is the population of interest to the plant scientist?

The yields in bushels per acre of the 5,000 fields

A farmer wants to determine if any of the pigs that he just finished weighing are outliers. The average weight of the pigs was 220 lb and the standard deviation of the weights was 40 lb. According to his records, one of the pigs weighed 420 lb. Calculate the z-score for this pig. Based on this z-score, is the weight of 420 lb an outlier?

The z-score for this pig is 5.0, and, therefore, he is an outlier.

Health care issues are receiving a greal deal of attention in both the academic and political arenas. A sociologist recently conducted a survey of senior citizens whose net worth is too high to quality for Medicaid, but who have no private health insurance. The ages (in years) of 8 uninsured senior citizens were as follows: Senior Citizen Age 1 66 2 70 3 64 4 88 5 74 6 72 7 87 8 79 Find the mode of the ages of these 8 senior citizens.

There is no mode for this dataset, because each number only appears once.

If an observation is found to be an outlier, it could be because the observation came from a different population (e.g., we are weighing Doberman Pincher dogs and the weight of a Cairn Terrier somehow got mixed in with the weights of the Dobermans).

True

If we identify an outlier in a dataset, it may be that the observation came from a different population (e.g., we are analyzing weights of Great Danes, but somehow the weight of a Dauschand got mixed in with our data).

True

Numerical descriptive measures of the relative frequency distribution for a population are called parameters.

True

The following is a valid probability distribution for a discrete random variable, X: X 0 1 2 3 P (X) 0.20 0.30 0.30 0.20

True

The probability of an event A is calculated by summing the probabilities of the sample points in the sample space for A.

True

The sample space for an experiment is the collection of all of the sample points.

True

Pie charts normally show the

proportion of observations falling in each class.

The heights in inches of young growing trees were measured at a nursery and used to construct the following stem-and-leaf display using the first digit as the stem and the second digit as the leaf: Stem Leaves 3 2 4 4 0 3 4 5 7 8 9 5 0 1 2 3 4 5 6 1 2 5 6 7 7 0 1 8 9 8 Construct a box plot for these data. The correct inner and outer fences for the box plot are _______, _______, _______, and _______.

lower outer fence = -15 lower inner fence = 15 upper inner fence = 95 upper outer fence = 125

What are the 3 measures of central tendency?

mean, median, mode