Stats, STATS CHAPTER 4, OPRE 6301 Test 1, OPRE HW#5, OPRE 6301 - 7, OPRE 6301 - 3, Stats 6301 - 1, OPRE 6301 Exam 1, CH4 QBA, Chapter 6 problems (FROM CH 6 HANDOUT)

If two events are independent, what is the probability that they both occur? Selected Answer: 0 0.50 1.00 Cannot be determined from the information given

Cannot be determined from the information given

If P(A) = 0.35, P(B) = 0.45, and P(A and B) = 0.25, then P(A|B) is: Selected Answer: 1.4 1.8 0.714 0.556

0.556

If A and B are mutually exclusive events with P(A) = 0.30 and P(B) = 0.40, then P(A or B) is: Selected Answer: 0.10 0.12 0.70 None of these choices

0.70

If P(A) = 0.65, P(B) = 0.58, and P(A and B) = 0.26, then P(A or B) is: Selected Answer: 1.23 0.97 0.18 0.11

0.97

Suppose P(A) = 0.50, P(B) = 0.75, and A and B are independent. The probability of the complement of the event (A and B) is: Selected Answer: .5 × .25 = .125 0.50 + .25 = .75 1 − (.50 + .25) = .25 1 − (.5 × .75) = .625

1 − (.5 × .75) = .625

If the two events are mutually exclusive and collectively exhaustive, what is the probability that one or the other occurs? Selected Answer: 0.00 0.50 1.00 Cannot be determined from the information given.

1.00

If two events are collectively exhaustive, what is the probability that one or the other occurs? Selected Answer: 0.00 0.50 1.00 Cannot be determined from the information given.

1.00

When the standard deviation is expressed as a percentage of the mean, the result is the coefficient of correlation. Selected Answer: True False

False

Your age group (1-9; 10-19; 20-29; 30-39; etc.) is an interval variable. Selected Answer: True False

False

Your final grade in a course (A, B, C, D, E) is a nominal variable. Selected Answer: True False

False

A sample of 20 observations has a standard deviation of 3. The sum of the squared deviations from the sample mean is: Selected Answer: 20. 23. 29. 171.

171

The interquartile range is the difference between the: Selected Answer: largest and smallest numbers in the data set. 25th percentile and the 75th percentile. median and the mean. None of these choices.

25th percentile and the 75th percentile.

The average score for a class of 30 students was 75. The 20 male students in the class averaged 70. The 10 female students in the class averaged: Selected Answer: 75. 85. 65. 70.

85

The Empirical Rule states that the approximate percentage of measurements in a data set (providing that the data set has a bell shaped distribution) that fall within two standard deviations of their mean is approximately: Selected Answer: 68%. 75%. 95%. 99%.

95%

Which measures of central location and variability are considered to be resistant to extreme values? Selected Answer: The mean and standard deviation. The mode and variance. The median and interquartile range. None of these choices.

The median and interquartile range.

If the observations are in the millions, a standard deviation of 10 would be considered small. If the observations are all less than 50, a standard deviation of 10 would be considered large. Selected Answer: True False

True

In a bell shaped distribution, there is no difference in the values of the mean, median, and mode. Selected Answer: True False

True

In a sample of 350 students selected from a large college of business, 25% are found to be marketing majors. The 25% is a statistic. Selected Answer: True False

True

Interval data may be treated as ordinal or nominal. Selected Answer: True False

True

Quartiles divide the observations in a data set into four parts with the same amount of data in each part. Selected Answer: True False

True

Suppose the probability that a person owns both a cat and a dog is 0.10. Also suppose the probability that a person owns a cat but not a dog is 0.20. The marginal probability that someone owns a cat is 0.30. Selected Answer: True False

True

The graph below is an example of a histogram. Selected Answer: True False

True

The intervals (classes) in a histogram do not overlap. Selected Answer: True False

True

The original observations cannot be determined once they are grouped into a frequency distribution. Selected Answer: True False

True

The standard deviation is expressed in terms of the original units of measurement but the variance is not. Selected Answer: True False

True

The sum of relative frequencies in a distribution always equals 1. Selected Answer: True False

True

You cannot calculate and interpret differences between numbers assigned to ordinal data. Selected Answer: True False

True

You think you have a 90% chance of passing your next advanced financial accounting exam. This is an example of subjective approach to probability

True

You think you have a 90% chance of passing your next advanced financial accounting exam. This is an example of subjective approach to probability. Selected Answer: True False

True

μ is a population parameter and is a sample statistic. Selected Answer: True False

True

A regular feature in many newspapers asks readers to respond via e-mail to a survey question. The percentages of yes and no responses are usually reported the following day. Should we ignore the results of these surveys? Explain.

Yes, we should ignore the results because this is an example of a self-selected sample. Self-selected samples are almost always biased because they tend to only represent those with strong opinions.

Generally speaking, if two variables are unrelated (as one increases, the other shows no pattern), the covariance will be: Selected Answer: a large positive number. a large negative number. a positive or negative number close to zero. None of these choices.

a positive or negative number close to zero.

The collection of all possible outcomes of an experiment is called: Selected Answer: a simple event a sample space a sample a population

a sample space

If the correlation coefficient r = 1.00, then all the observations must fall exactly on: Selected Answer: a straight line with a slope that equals 1.00. a straight line with a negative slope. a straight line with a positive slope. a horizontal straight line with a zero slope.

a straight line with a positive slope.

For what type of data are frequencies the only calculations that can be done? Selected Answer: a. Interval data b. Nominal data c. Ordinal data d. None of these choices.

b. Nominal data

The length of the box in the box plot portrays the: Selected Answer: median. interquartile range. range. third quartile.

interquartile range.

The probability of the intersection of two events A and B is denoted by P(A and B) and is called the: Selected Answer: marginal probability joint probability conditional probability of A given B conditional probability of B given A

joint probability

Which of the following is a property of r, the coefficient of correlation? Answers: r always lies between 0 and 1. r has no units. If you switch the values of X and Y, the sign of r changes. All of these choices are true.

r has no units.

The distance between the 25th percentile and the median is always the same as the distance between the median and the 75th percentile. Selected Answer: True False

False

The probability of the union of two mutually exclusive events A and B is 0. Selected Answer: True False

False

The response rate of a survey is the proportion of all people who were selected but did not complete the survey. Selected Answer: True False

False

When a distribution has more values to the left and tails off to the right, it is skewed negatively. Selected Answer: True False

False

The value of the standard deviation may be either positive or negative, while the value of the variance will always be positive. Selected Answer: True False

False

Which of the following represents a population, as opposed to a sample? Selected Answer: a. Every fourth student to arrive at the book store on your campus. b. 2,000 respondents to a magazine survey which has 600,000 subscribers. c. The first 15 students in your class completing a final exam. d. All registered voters in the state of West Virginia

. d. All registered voters in the state of West Virginia

A and B are disjoint events, with P(A) = 0.20 and P(B) = 0.30. Then P(A and B) is: Selected Answer: 0.50 0.10 0.00 0.06

0.00

If two events are mutually exclusive, what is the probability that both occur at the same time? Selected Answer: 0.00 0.50 1.00 Cannot be determined from the information given.

0.00

If an experiment consists of five outcomes with P(O1) = 0.10, P(O2) = 0.20, P(O3) = 0.30, P(O4) = 0.15, then P(O5) is Selected Answer: 0.75 0.25 0.50 Cannot be determined from the information given.

0.25

Which of the following is a measure of variability? Selected Answer: The interquartile range The variance The coefficient of variation All of these choices are true.

All of these choices are true.

Which of the following statements is true regarding the data set 8, 8, 8, 8, and 8? Selected Answer: The range equals 0. The standard deviation equals 0. The coefficient of variation equals 0. All of these choices are true.

All of these choices are true.

At the end of a safari, the tour guide asks the vacationers to respond to the questions listed below. For each question, determine whether the possible responses are interval, nominal, or ordinal. a. How many safaris have you taken prior to this one? b. Do you feel that your tour safari lasted sufficiently long (yes/no)? c. Which of the following features of the accommodations did you find most attractive: location, facilities, room size, service, or price? d. What is the maximum number of hours per day that you would like to spend traveling? e. Is your overall rating of this safari: excellent, good, fair, or poor?

Correct Answer: a. Interval b. Nominal c. Nominal d. Interval e. Ordinal

"Wouldn't you agree that foreign cars are better than American cars?" is an example of a well-worded survey question. Selected Answer: True False

False

A descriptive measure of a sample is called a parameter. Selected Answer: True False

False

A resort employs 3,500 managers and staff. To ascertain their employees' opinions of a proposed health insurance plan, 350 employees are surveyed at random. The proportion of the 350 employees who favor the health insurance plan represents a parameter in this scenario. Selected Answer: True False

False

Assume that A and B are independent events with P(A) = 0.30 and P(B) = 0.50. The probability that both events will occur simultaneously is 0.80. Selected Answer: True False

False

Experience shows that few students hand in their statistics exams early; most prefer to hand them in near the end of the test period. This means the time taken by students to write exams is positively skewed. Selected Answer: True False

False

If the coefficient of correlation r = 0 between two variables, then there can be no relationship whatsoever between these two variables. Selected Answer: True False

False

If we draw a straight line through the points in a scatter diagram and most of the points fall close to the line, there must be a positive relationship between the two variables. Selected Answer: True False

False

In a histogram, each observation is assigned to one or more classes. Selected Answer: True False

False

In a sample of 350 Students selected from a large college of business, 25% are found to be marketing majors. The 25% is a parameter. Selected Answer: True False

False

P(A) + P(B) = 1 for any events A and B that are mutually exclusive. Selected Answer: True False

False

Can a scatter diagram be used to explore the relationship between two nominal variables? Explain why or why not.

No; scatter diagrams plot points of X and Y when both variables are interval variables. You cannot talk about a nominal variable increasing or decreasing.

The Chairman of a College of Business with five departments wants to estimate the average number of student-hours lost per month due to illness of their professors. Describe a sampling plan that will help the Dean compare the average student-loss hours for the five departments.

The Chairman can take one simple random sample from each department for comparison purposes. That means he is taking a stratified random sample, where the strata are the five departments.

35% of a sample of 300 professional baseball players indicated that their parents did not play baseball. Based on this sample, we estimate that approximately 35% of the parents of all professional baseball players did not play baseball, plus or minus 5%. This is an example of using inferential statistics. Selected Answer: True False

True

A histogram is said to be symmetric if, when we draw a vertical line down the center of the histogram the two sides are nearly identical. Selected Answer: True False

True

A population is the group of all items of interest to a statistics practitioner. Selected Answer: True False

True

A statistic is typically a known quantity while a parameter is typically an unknown quantity. Selected Answer: True False

True

An experiment involves collecting data about persons or objects by deliberately exposing them to some kind of change and comparing the results. Selected Answer: True False

True

Bayes' Law is a formula for revising an initial subjective (prior) probability value on the basis of new results, thus obtaining a new (posterior) probability value. Selected Answer: True False

True

Experimental data tend to be more reliable, or "stronger," than survey data. Selected Answer: True False

True

If A and B are independent events with P(A) = .40 and P(B) = .50, then P(A and B) = .20. Selected Answer: True False

True

If either Event A or Event B (but not both) must occur, then A and B are mutually exclusive and collectively exhaustive events.

True

If the coefficient of correlation r = −.81, the standard deviations of x and y are 20 and 25, respectively, then cov(x, y) must be −405.0. Selected Answer: True False

True

If the distribution of a data set were perfectly symmetric, the distance from Q1 to the median would always equal the distance from Q3 to the median in a box plot. Selected Answer: True False

True

The personnel director at a large company studied the eating habits of the company's employees. The director watched and recorded whether each employee brought his/her own lunch to work, ate at the company cafeteria, or went out to lunch. What method of data collection was used here? Selected Answer: a. Direct observation. b. An experiment. c. A survey. d. A personal interview.

a. Direct observation.

All calculations are permitted on what type of data? Selected Answer: Answers: a. Interval data b. Nominal data c. Ordinal data d. All of these choices are true.

a. Interval data

Which of the following best describes the concept of marginal probability? Selected Answer: a. It is a measure of the likelihood that a particular event will occur, regardless of whether another event occurs. b. It is a measure of the likelihood that a particular event will occur, if another event has already occurred. c. It is a measure of the likelihood of the simultaneous occurrence of two or more events. d. None of these choices.

a. It is a measure of the likelihood that a particular event will occur, regardless of whether another event occurs.

Which of the following causes sampling error? a. Taking a random sample from a population instead of studying the entire population. b. Making a mistake in the process of collecting the data. c. Self-selection bias d. All of the above

a. Taking a random sample from a population instead of studying the entire population.

Which of the following statements is true for the following observations: 7, 5, 6, 4, 7, 8, and 12? Selected Answer: a. The mean, median and mode are all equal. b. Only the mean and median are equal. c. Only the mean and mode are equal d. Only the median and mode are equal.

a. The mean, median and mode are all equal.

In a histogram, the proportion of the total area which must be to the left of the median is: Answers: a. exactly 0.50. b. less than 0.50 if the distribution is negatively skewed. c. more than 0.50 if the distribution is positively skewed. d. unknown.

a. exactly 0.50.

The classification of student class designation (freshman, sophomore, junior, senior) is an example of a(n) Selected Answer: a. ordinal random variable. b. interval random variable. c. nominal random variable. d. a parameter.

a. ordinal random variable.

If two data sets have the same range: Selected Answer: a. the distances from the smallest to largest observations in both sets will be the same. b. the smallest and largest observations are the same in both sets. c. both sets will have the same standard deviation. d. both sets will have the same interquartile range.

a. the distances from the smallest to largest observations in both sets will be the same.

Which of the following represents a graphical presentation of interval data? Selected Answer: a. A bar chart. b. A histogram. c. A pie chart. d. All of these choices are true.

b. A histogram.

A marketing research firm selects a random sample of adults and asks them a list of questions regarding their beverage preferences. What type of data collection is involved here? Selected Answer: a. An experiment. b. A survey. c. Direct observation. d. None of these choices.

b. A survey.

Which of the following statements about the mean is not always correct? Selected Answer: a. The sum of the deviations from the mean is zero. b. Half of the observations are on either side of the mean. c. The mean is a measure of the central location. d. The value of the mean times the number of observations equals the sum of all observations.

b. Half of the observations are on either side of the mean.

A random sample of 100 students is taken at LearnAll University and it's found that their average GPA is 3.1. If this information is used to help estimate the average GPA for all students at LearnAll University, which branch of statistics was applied? Selected Answer: a. Population statistics b. Inferential statistics c. Sample statistics d. Descriptive statistics

b. Inferential statistics

Which of the following must be avoided in designing a survey? Selected Answer: a. Dichotomous questions. b. Leading questions. c. Demographic questions. d. All of these choices are true.

b. Leading questions.

In a negatively skewed distribution, which of the following is the correct statement? Selected Answer: a. The distance from Q1 to Q2 is smaller than the distance from Q2 to Q3 b. The distance from the smallest observation to Q1 is larger than the distance from Q3 to the largest observation c. The distance from the smallest observation to Q2 is smaller than the distance from Q2 to the largest observation d. The distance from Q1 to Q3 is twice the distance from the Q1 to Q2

b. The distance from the smallest observation to Q1 is larger than the distance from Q3 to the largest observation

Which of these measures of central location is not sensitive to extreme values? Answers: a. The mean b. The median c. The mode d. All of these choices are true.

b. The median

A researcher at Florida International University (FIU) wants to estimate the average number of credits earned by students last semester at FIU. She randomly selects 750 students from last semester and finds that they averaged 13.75 credits per student. The population of interest to the researcher is: Selected Answer: a. the 750 FIU students selected at random. b. all FIU students enrolled last semester. c. all FIU students. d. all college students.

b. all FIU students enrolled last semester.

The length of the box in the box plot portrays the: a. Median b. interquartile range c. range d. third quartile

b. interquartile range

A company has developed a new power cell and wants to estimate its average lifetime. A random sample of 650 power cells is tested and the average lifetime of this sample is found to be 315 hours. The 315 hours is the value of a: Selected Answer: a. parameter. b. statistic. c. sample. d. population.

b. statistic.

A modal class in a histogram is the class that includes Selected Answer: a. the largest observation in the data set. b. the largest number of observations. c. the smallest number of observations. d. the smallest observation in the data set.

b. the largest number of observations.

Which method of data collection is involved when a researcher counts and records the number of students wearing backpacks on campus in a given day? a. A survey b. An experiment c. An observational study d. None of the above

c. An observational study

What values are displayed on a cumulative relative frequency distribution? Selected Answer: a. The proportion of observations that fall into each class interval. b. The number of observations that fall below each class interval. c. The proportion of observations that fall below each class interval. d. The number of observations that fall into each class interval.

c. The proportion of observations that fall below each class interval.

If A and B are mutually exclusive events with P(A) = 0.70, then P(B): Selected Answer: can be any value between 0 and 1. can be any value between 0 and 0.70. cannot be larger than 0.30. equals 0.30.

cannot be larger than 0.30.

The strength of the linear relationship between two interval variables can be measured by the: Selected Answer: coefficient of variation. coefficient of correlation. slope of the regression line. Y-intercept.

coefficient of correlation.

In a perfectly symmetric bell shaped "normal" distribution: Selected Answer: a. the mean equals the median. b. the median equals the mode. c. the mean equals the mode. d. All of these choices are true.

d. All of these choices are true.

A study is underway to determine the average height of all 29,000 adult pine trees in a certain national forest. The heights of 600 randomly selected adult pine trees are measured and analyzed. The parameter in the study is: Selected Answer: a. all the adult pine trees in this forest. b. the average height of the 600 randomly selected adult pine trees. c. the 600 adult pine trees selected at random from this forest. d. the average height of all the adult pine trees in this forest.

d. The average height of all the adult pine trees in this forest.

If A and B are independent events with P(A) = 0.60 and P(A/B) = 0.60 then P(B) is: a. 1.20 b. 0.60 c. 0.36 d. cannot be determined with the information given

d. cannot be determined with the information given

In a histogram, the proportion of the total area which must be to the right of the mean is:

exactly 0.50 if the distribution is symmetric and unimodal.