AREC 239 All quizzes (1-18)

Evaluate these statements regrading events A and B in the Venn diagram below: (i) A and B are disjoint (ii) A and B are dependent (iii) A and B are complements of each other The picture has 2 circles A and B and they DON'T intersect. (i) is true; (ii) and (iii) are false (iii) is true; (i) and (ii) are false (ii) is true; (i) and (iii) are false (i) and (ii) are true; (iii) is false (i), (ii), and (iii) are all true (i), (ii), and (iii) are all false

(i) and (ii) are true; (iii) is false

Suppose Z has standard normal distribution. Consider these three statements: (i) P(Z < -1.5 ) = P( Z > 1.5) (ii) P(Z < -1.5 ) = 1 - P( Z < 1.5) (iii) P(Z > -1.5 ) = P(Z < 1.5 ) Then (i) is true; (ii) and (iii) are false (ii) is true; (i) and (iii) are false (iii) is true; (i) and (ii) are false (i) and (ii) are true; (iii) is false (i) and (iii) are true; (ii) is false (ii) and (iii) are true; (i) is false (i), (ii) and (iii) are all true (i), (ii) and (iii) are all false

(i), (ii) and (iii) are all true

Calculate sample correlation coefficient for the following sample data: (x,y) 5,5 6,3 10,0 11,1 8,2 10,2

-0.879

John scored 80 points in an exam. The class average is 90 and class variance is 16. Compute John's z score? Note that variance (and not standard deviation) is given.

-2.5

If A and B are mutually exclusive, P(A) = 0.2, and P(B) doesn't equal 0, then P(A|B) = 0 0.8 0.2 1 Not enough information is given to figure if any of the other alternatives are correct

0

A fair coin is tossed twice. Let X represent the total number of heads from the two tosses. What are the possible values X can take? 1,2,3 0,1,2 1,2 0,1

0,1,2

Suppose random variable z has standard normal distribution. Then what is p(z = -1.25)? 0.1056 0.4522 0 0.8944

0.1056

Many American home owners display U.S. flag in their front yard to show their patriotism. In a particular U.S. state 60% of home owners are republicans. A survey indicates that 40% of republicans and 20% of other home owners display flags. What is the probability that a randomly selected home owner displays a flag? Hint: Defining these events might help you. Let R = Randomly selected home owner is a republican and let F = Randomly selected homeowner displays a flag. Hint: Use law of total probability

0.24+0.08 = 0.32

A fair coin is tossed twice. Let X represent the total number of heads from both tosses. What is the prob(x = 0)? 0.75 0.5 0.25 0

0.25

John is a NCAA basketball player. The number of fouls he commits in a game is random. The following is the probability distribution for the number of fouls John commits in a game: Number of Fouls=Probability 0=0.05 1=0.10 2=0.15 3=0.20 4=0.25 5=?? What is the probability that he fouls out of the game? Note: A player fouls out if he commits five fouls in a game. 0.25 0.70 0.75 1 0 0.30

0.25

Suppose Z has standard normal distribution. What is P(Z < -0.44)? 0.33 0.3446 -0.15 0.67

0.33

Many American home owners display U.S. flag in their front yard to show their patriotism. In a particular U.S. state 60% of home owners are republicans. A survey indicates that 40% of republicans and 20% of other home owners display flags. What is the probability that a randomly selected home owner is not a republican? Hint: Defining these events might help you. Let R = Randomly selected home owner is a republican and let F = Randomly selected homeowner displays a flag.

0.4

Many American home owners display U.S. flag in their front yard to show their patriotism. In a particular U.S. state 60% of home owners are republicans. A survey indicates that 40% of republicans and 20% of other home owners display flags. What is the probability that a randomly selected home owner is not a republican and displays a flag? Hint: Defining these events might help you. Let R = Randomly selected home owner is a republican and let F = Randomly selected homeowner displays a flag.

0.4(0.2)= 0.08

A fair coin is tossed twice. What is the probability that you get heads on the second toss given that the coin landed tails on the first toss? 0.5 0.25 0.75 1 0

0.5

Suppose random variable z has standard normal distribution. Then what is prob(z > 0)? 0 1 0.5 More information is needed to answer this question.

0.5

Many American home owners display U.S. flag in their front yard to show their patriotism. In a particular U.S. state 60% of home owners are republicans. A survey indicates that 40% of republicans and 20% of other home owners display flags. What is the probability that a randomly selected home owner is a republican? Hint: Defining these events might help you. Let R = Randomly selected home owner is a republican and let F = Randomly selected homeowner displays a flag.

0.6

Many American home owners display U.S. flag in their front yard to show their patriotism. In a particular U.S. state 60% of home owners are republicans. A survey indicates that 40% of republicans and 20% of other home owners display flags. What is the probability that a randomly selected home owner is a republican and displays a flag? Hint: Defining these events might help you. Let R = Randomly selected home owner is a republican and let F = Randomly selected homeowner displays a flag.

0.6(0.4) = 0.24

In a large state, 5% individuals are infected with corona virus. Suppose a particular test used for detecting the corona virus detects the virus 93% of the time (i.e., if someone has corona virus, the test detects it 93% of the time; the remaining 7% of the time the test gives false negative). But the test also gives a false positive 3% of the time. Suppose a randomly selected individual tests positive for the corona virus. Given this test result, what is the probability that the individual is actually infected with corona virus? 0.58 3/7 0.62 0.90 0.93 0.075

0.62

Suppose that the correlation between a set of scores X and a set of scores Y is equal to 0.65. If the scores are switched, so that the X scores become the Y scores, and the Y scores become the X scores, what would the new correlation between the scores be? -0.35 0.35 0 0.65 -0.65

0.65

Number of students that show up during Dr. Aradhyula's office hours is random. The probability distribution for the number of students that show up is given below. Number of Students=Probability 0=0.6 1=0.18 2=0.12 3=0.06 4=0.04 How many students can Dr. Aradhyula expect during office hours? That is, what is the expected value of number of students? 0 1.36 2 2.5 0.76

0.76

The probability distribution for the number of goals the Lions soccer team makes per game is given below. Number of Goals=Probability 0=0.05 1=0.15 2=0.35 3=0.30 4=0.15 What is the probability that in a given game the Lions will score at least 1 goal? 0.95 0.05 0.15 1.0 0.20 0.55

0.95

Many American home owners display U.S. flag in their front yard to show their patriotism. In a particular U.S. state 60% of home owners are republicans. A survey indicates that 40% of republicans and 20% of other home owners display flags. Suppose you drive around and notice a house with a flag in the front yard. What is the probability that this particular house owner is a republican? What is what is the probability a home owner is a republican given that a flag is displayed in the front yard? Hint: Defining these events might help you. Let R = Randomly selected home owner is a republican and let F = Randomly selected homeowner displays a flag.

1- (0.08/0.32) = 0.75

Let x represent the number of days it rains in a year in Timbuktu. Meteorologists have estimated the following probability distribution for x. x=f(x) 0=0.5 1=0.1 2=0.1 3=0.1 4=0.1 5=0.1 Based on these probabilities what is the expected number of days it rains in Timbuktu? 2.5 0.30 1.5 0 0.25 3

1.5

From a standard deck of playing cards, one card is drawn randomly. What is the probability that the card is a queen? Note (In case you do not know about cards): A standard deck of playing cards consists of 52 cards in each of the 4 suits of clubs (♣), diamonds (♦), hearts (♥) and spades (♠). Clubs and Spades are black while Hearts and Diamonds are red. Each suit contains 13 cards: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King. 1/4 1/52 1/2 1/8 1/13

1/13

The variance of a sample of 169 observations equals 576. The standard deviation of the sample equals: 3.408 13 576 3.42857 331776 28461 24

24

An experiment consists of tossing 5 coins successively. The number of sample points in this experiment is 10 2 25 4 16 32

2^5 = 32

The density curve for X shown below takes value 0.5 on the interval 0≤X≤2 and takes the value 0 everywhere else. That is, X has a uniform distribution as show below. What percent of observations lie between 0.5 and 1.2? 35% 70% 50% 120% 68%

35%

Your favorite football team has 2 games left to finish the season. The outcome of each game for your team can be win, lose or tie. The number of possible outcomes from these two games is 6 4 9 3 5 2

3^2 = 9

From a standard deck of playing cards, one card is drawn randomly. What is the probability that the card is not a Jack? Note: A standard deck of playing cards has 52 cards organized into 4 suits: Clubs (♣), Diamonds (♦), Hearts (♥) and Spades (♠). Clubs and Spades are black while Hearts and Diamonds are red. Each suit contains 13 cards: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King. 4/52 48/52 1/52 4/13 51/52

48/52

Random variable X takes values of 4 and 8 with probabilities 0.25 and 0.75, respectively. What is the expected value of X? 5 6 12 7

7

A random of sample of five students is selected from a large class and their marks in an exam are 70, 75, 88, 85 and 82. Compute the sample standard deviation.

7.38

A survey is taken among customers of a fast-food restaurant to determine their preference for hamburger or chicken. Of 200 respondents selected, 75 were children and 125 were adults. 120 preferred hamburger and 80 preferred chicken. 55 of the children preferred hamburger. What is the probability that a randomly selected individual prefers chicken given that the individual is an adult? 25/125 125/200 60/200 60/80 60/125 80/200

75 Children: 55 hamburger, 20 chicken 125 Adults: 65 hamburger, 60 chicken 60/125

Bob scored 82 points in an exam that placed him at 91st percentile. What can you infer from this information? 91 people in the class scored 82 points or below in the exam 82 percent of people in the class scored 91 or below 91 percent of people in the class scored 82 points or below Bob scored 91% in the exam Bob is a nice guy

91 percent of people in the class scored 82 points or below

Suppose events A and B are such that P(A) + P(B) = P(A∪B). From we can conclude that A and B are dependent A and B are independent A and B are complements None of the above

A and B are dependent

Professor Dingbat's last exam was particularly hard. The class average was only 40 and variance was 16. Professor Dingbat decided to add 10 points to the scores of all the students. A new class mean and variance were calculated after this addition of 10 points. As a result of adding 10 points to the scores of all students, mean increases by 10 points but variance remains unchanged. mean increases by 10 points but variance increases 100 times. both mean and variance remain unchanged. both mean and variance increase by 10 points

Adding a constant does not change variance and standard deviation.

Which of the following is true? -Census measures each person in the specific population. -Sample measures a subset of the population. -Since samples are used in statistics to make inferences about the population, it is desirable for the sample to be representative of the population. -All of the above

All of the Above

The pie chart below summarizes the results of a survey of 300 randomly selected students at a particular high school. In the survey, each student is asked to name their most preferred brand of soft drink. What is a reasonable conclusion from this chart? 20%-other 15%-Dr. Pepper 10%-Sprite 25%-Pepsi 30%-coke -Coke is the most preferred brand of soft drink in the high school -Coke and Pepsi account for more than half of the students in the sample -Out of 300 students surveyed, 45 students prefer Dr. Pepper -All of the above

All of the above

Two events A and B are independent if P(A|B) = P(A) P(B|A) = P(B) P(A)P(B) = P(A∩B) All of the above

All of the above

Suppose X is a continuous random variable defined over the interval 2 to 20. Consider these statements: (i) p(x = 11) = 0 (ii) p(x≤ 6.5) = p(X <6.5) Which of the following is true? (i) is true; (ii) is false (ii) is true; (i) is false Both (i) and (ii) are true Both (i) and (ii) are false

Both (i) and (ii) are true

Many American home owners display U.S. flag in their front yard to show their patriotism. In a particular U.S. state 60% of home owners are republicans. A survey indicates that 40% of republicans and 20% of other home owners display flags. According to these numbers, are the activities of displaying flags and party affiliation independent or dependent?

Dependent

What is the probability of getting three tails in three flips of a fair coin? 0.25 0.5 0.125 0.75 0.875 1/6

Each flip has (1/2) of getting tails. So getting 3 tails in 3 flips is (1/2)^3 = 0.125 0.125

A data set consisting of many observations of a single characteristic is a categorical data set. True or False?

False

Compared to mean, median is more sensitive to the presence of outliers True or False?

False

Sample standard deviation does not depend on the units of measurements of the variable. True or False?

False

The entire collection of individuals or objects about which information is desired is called a sample. True or False?

False

The relative frequency for a particular category is the number of times the category appears in the data. True or False?

False

When drawing a histogram, the number of bins should equal the number of observations. True or False?

False

Which of the following statements is/are true? - I. Categorical variables are the same as qualitative variables. - II. Categorical variables are the same as continuous variables. - III. Quantitative variables can be continuous variables.

I and III

A fair coin is tossed twice. Let X represent the total number of heads from both tosses. Here, E(X) = 1. What does an expected value of 1 mean? Note: In the following, tossing a fair coin twice is called "game." -If this game were to be played many number of times, on an average we get 1 head per game. -Every time this game is played, we get exactly one head.

If this game were to be played many number of times, on an average we get 1 head per game.

Suppose P(A|B) = P(A). Then events A and B are said to be dependent independent complements disjoint

Independent

Kelly just took midterm exam in her chemistry class that has 500 students. Kelly obtained a z-score of -1.5 in the test. Which of the following is true? Kelly's actual raw score is 1.5 standard deviations above the class mean Kelly's score is among the lowest 75 students in the class Kelly's score is among the lowest 8 students in the class Kelly's actual raw score is less than the class mean Kelly's score is 1.5 points less than the class mean

Kelly's actual raw score is less than the class mean

Which of the following provides a measure of central location for the data? standard deviation mean range variance

Mean

A sample has 51 observations. The data are sorted from the smallest value to the largest value. The smallest value and the largest value are dropped from the sample resulting in a new sample that has only 49 observations. Which of the following is necessarily true? -Median for the new sample = median for the old sample -Mean for the new sample = mean for the old sample -Both of the above are true -None of the above

Median for the new sample = median for the old sample

An animal scientist is studying cows. She collected information on weight (in pounds), breed, age (measured in months), and milk production (measured in pounds) for each of the 130 cows in a herd. This data is an example of: Categorical Data Multivariate Data Qualitative Data Univariate Data

Multivariate Data

This question is left blank no 68.

No question 68

This question is left blank no 69.

No question 69

This question is left blank no 70.

No question 70

Suppose random variable y can take three possible values: 10, 20 and 30. Is the following a valid probability distribution for y? y=P(y) 10=0.5 20=0.3 30=0.4 No, it is not a valid probability distribution for y because sum of probabilities is not 1. Yes, it is a valid probability distribution for y.

No, it is not a valid probability distribution for y because sum of probabilities is not 1.

Is the following a valid probability distribution for random variable x? x=P(x) 2=0.5 3=-0.2 4=0.7 Yes. It is because the sum of probabilities is equal to 1 No. It is not because one of the probabilities is negative.

No. It is not because one of the probabilities is negative.

In the following Venn diagram, A represents all students enrolled in Algebra class and B represents all students enrolled in Biology class. The rectangle represents all students in the school. The figure has 2 circles A and B intersected in between. Only part B is shaded. Which of the following statements is true? -Shaded area in the Venn diagram represents all students who are neither in Algebra nor in Biology -Shaded area in the Venn diagram represents A union B -Shaded area in the Venn diagram represents A complement -Shaded area in the Venn diagram represents A intersection B -None of the above

None of the above

Suppose P(A) = 0.5 and P(B) = 0.6. The probability that both A and B will occur is 0.1. From this we can conclude that: A and B are independent A and B are disjoint A and B are complements to each other None of the above

None of the above

Which of the following is NOT considered a part of statistics discipline? -Collecting data -Analyzing data and displaying data graphically -Making inferences (generalizations) from the collected data -None of the above

None of the above

Which of the following is NOT true regarding standard normal distribution? Mean of the distribution is 0. Variance of the distribution is 1 Standard deviation of the distribution is 1. The probability distribution curve never touches the x-axis; in the tails, it ever so closely gets to x-axis but never quite touches the x-axis. None of the above.

None of the above.

Which of the following is a discrete random variable? The average night time temperature in July in a randomly selected city The weight of a randomly selected heifer on a ranch Number of apps on a randomly selected smart phone The height of a randomly selected California redwood tree

Number of apps on a randomly selected smart phone

The conditional probability of B given A is defined by the formula: P(B∩A)/P(B) P(B)/P(A) P(B∪A)/P(A) P(A∩B)/P(A)

P(A∩B)/P(A)

In a game, a fair six-sided die is tossed and you are paid the square of the number that shows up. For example, if 5 shows up, you are paid $25. It costs $15 to play this game. If you play this game thousands of times, you expect to come out even. you expect to lose money; you will not come out ahead. you expect to win money; you will come out ahead.

Payoff could be $1, $4, $9, $16, $25, or $36 with probabilities 1/6 each. So expected payoff = 1(1/6) + 2(1/6) + 3(1/6) +4(1/6) +5(1/6) +6(1/6) = $15.166667. It costs $15 to play this game. So expected net payoff = 15.166667 - 15 = $0.166667 > 0. So you will come out ahead. Note: Expected pay off is not square of 3.5. you expect to win money; you will come out ahead.

The entire collection of individuals or objects about which information is desired is called Sample Statistic Population Stratum

Population

Which of the following would be greatly affected by outliers? IQR Range Median

Range

By definition a subset of a population selected for study is a: -census -population -outlier -sample

Sample

Consider the distribution of SAT scores of all applicants to Harvard University. What shape do you expect for this distribution? Note: Many students with poor SAT scores do not bother applying to Harvard because it is so competitive. Skewed to the right Skewed to the left Symmetric

Skewed to the left

Which of the following represents distribution of age at death of people in USA?

Skewed to the left graph

An investor wants to purchase stock on the New York Stock Exchange. It is desired that the stock be very stable, meaning that the price of the stock remains approximately the same from day to day, with very little change. If the investor decides to track a number of stocks to observe stability before purchasing, which measurement would be most appropriate to compute? Median Mode Standard Deviation Mean

Standard Deviation

In the following Venn diagram, A represents all students enrolled in Algebra class and B represents all students enrolled in Biology class. The rectangle represents all students in the school. The figure has 2 circles A and B intersected in between. Circle A and B are shaded but not the intersection. The shaded area in the above Venn diagram represents what? who are in Algebra but not in Biology Students who are in Algebra or in Biology but not in both Students who are neither in Algebra nor in Biology Students who are in Biology but not in Algebra Students who are in Algebra or in Biology or in both

Students who are in Algebra or in Biology but not in both

Which of the following is always true for any given sample? Sum of the deviations of the individual data elements from the sample mean is zero Sample mean is greater than sample median Interquartile range is a negative number Sum of squares is always equal to square of the sum

Sum of the deviations of the individual data elements from the sample mean is zero

What can you infer from the density curve given below? The graph looks like upsidedown U with the starting and ending points are (1,0), (11,0). The height in between is 0.150 The curve is normal. The density curve is symmetric. The density curve is skewed to the left. The density curve is skewed to the right.

The density curve is symmetric.

Which of the following random variables is NOT discrete? The number in a group of 20 people who have college degrees The number of courses in which a college student is enrolled The distance traveled by a motorcycle on one gallon of gas The number of attempts needed in order to successfully complete a task

The distance traveled by a motorcycle on one gallon of gas

In your top dresser drawer are 3 white socks and 3 black socks, unpaired and mixed up. You pull two socks randomly, at once, from the drawer. What is the probability that you have a pair of white socks? 1/6 1/2 1/4 2/5 1/5 3/10

The first probability of a white sock is (3/6), since this is dependent event, the second probability is (2/5). Since we want to have them together, you multiply them: (3/6)*(2/5) = (6/30) = 1/5 1/5

Find the scatter diagram that corresponds to the correlation coefficient r = -0.02

The graph that looks like scattered with zero slope

Which of the following random variables is NOT continuous? The number of fumbles in a football game The length of life of a 60-watt light bulb The birth weight of a newborn baby Time from take-off to landing of an airline flight The velocity of an asteroid

The number of fumbles in a football game

A bag has 4 green marbles and 6 red marbles. Two marbles are drawn without replacement. What is the probability that the second marble is green given that the first one is red? 18/100 4/9 4/10 4/6 1/5 24/100 24/90

The probability for the first draw is (6/10). The second probability is (4/9). Since the question only refers to the second sock being green the probability is (4/9) 4/9

In a carnival, there is a game where a player tosses a die and wins a prize if number 1 shows up. However, on Tuesday evenings, if the toss is a 6, the player is allowed to toss again. What effect does this have on the player's probability of winning the prize? The probability will decrease The probability will increase The probability will remain the same

The probability will increase

Two six-sided dice are rolled and their sum is taken. What is the probability that the sum is not seven? Hint: First, calculate the probability that the sum is seven. 1/36 5/6 1/11 0 1/6 12/36 4/36 1

There are 36 possible outcomes in total. To GET a SEVEN, there are only 6 cases: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). So the remaining cases left are 30/36 = 5/6 5/6

Suppose that, from a sample of 200 college students, each student's grade point average and parents' income level was compared. The correlation coefficient was calculated to be r= 0.17719. Which of the following is the best description of the meaning of this correlation coefficient? -There is a strong negative linear relation between grade point average and parents' income level. -There is a weak negative linear relation between grade point average and parents' income level. -There is no relation -- linear or non-linear -- between grade point average and parents' income level. -There is a weak positive linear relation between grade point average and parents' income level. -There is a very strong linear relation between grade point average and parents' income level.

There is a weak positive linear relation between grade point average and parents' income level.

A bag has 4 green marbles and 6 red marbles. One marble is drawn randomly from this bag. What is the probability that it is a green marble? 1/10 5/10 1/4 6/10 4/10

Total number of marbles are 10. So you can get only 4 green out of 10. 4/10

A data set is discrete if the possible values are isolated points on the number line. True or False?

True

A primary use of inferential statistics is to make generalizations from a sample to a population. True or False?

True

Correlation coefficient between two variables does not depend on the units of measurement of both variables True or False?

True

If A and B are disjoint, then the probability(A intersection B) = 0 True or False?

True

If sample correlation coefficient is close to 1, then sample points in the scatter plot lie close to a straight line with positive slope. True or False?

True

One advantage of histograms is that they can be used for large datasets with many observations. True or False?

True

Saying that two events are mutually exclusive is the same thing as saying the events are disjoint. True or False?

True

Draw scatter plot for the following data. (x,y) 5,5 6,3 10,0 11,1 8,2 10,2

Use excel to do this.

Consider random variable w. Is the following a valid probability distribution for w? w=P(w) -10=0.5 10=0.3 20=0.2 Yes, it is a valid probability distribution for w No, it is not a valid distribution for w

Yes, it is a valid probability distribution for w

Suppose you are computing sample correlation coefficient for a sample of 100,000 observations and obtained a sample correlation coefficient value of 2.6. What does it mean? -You have too many observations -There is a strong negative linear association between the two variabes -You made a mistake in your computations -There is a strong positive linear association between the two variables

You made a mistake in your computations

Suppose events A and B are complements to each other. Then consider the following two statements and decide which one(s) is (are) true? (i) P(A) + P(B) = 1 (ii) P(A∩B)=0 -both (i) and (ii) are false -(i) is true; (ii) is false -both (i) and (ii) are true -(ii) is true; (i) is false

both (i) and (ii) are true

When data are positively skewed, the mean will usually be equal to the median greater than the median smaller than the median positive

greater than the median

During a cold winter, the temperature stayed below zero for ten days, ranging from -20 to -5. The variance of the temperatures of the ten-day period can be either negative or positive is negative since all the numbers are negative is positive cannot be computed since all the numbers are negative

is positive

The interquartile range is: (i) Another name for variance (ii) Can never be negative (iii) A measure of variability only (i) is true; (ii) and (iii) are not true only (ii) is true; (i) and (iii) are not true only (ii) and (iii) are true; (i) is not true only (iii) is true; (i) and (ii) are not true

only (ii) and (iii) are true; (i) is not true

Fifty employees at the University of Arizona responded to a survey asking for the number of minutes they commute to work in the morning. Eighteen employees indicated that their commutes are 15 to less than 20 minutes. The relative frequency for this class in a frequency distribution would be 0.40 0.36 0.30 0.18 0.75 0.09

relative frequency:(number observed)/(total) = 18/50 =0.36

Suppose you are computing sample correlation coefficient between x and y and obtained a value of -0.94. Which of the following is true? -x and y show a negative linear relationship, i.e., higher values of x are generally associated with lower values of y -x and y show a negative linear relationship, i.e., lower values of x are generally associated with lower values of y -You made a mistake in computations because correlation coefficient cannot be negative -x or y or both take negative values

x and y show a negative linear relationship, i.e., higher values of x are generally associated with lower values of y