Question:* What is the median of: 5, 10, 15?
Answer: • 10
Question:* What is the most commonly used statistical measure of spread in a normally-distributed population?
Answer: • standard deviation
Question:* An auto analyst is conducting a satisfaction survey, sampling from a list of 10,000 new car buyers. The list includes 2,500 Ford buyers, 2,500 GM buyers, 2,500 Honda buyers, and 2,500 Toyota buyers. The analyst selects a sample of 400 car buyers, by randomly sampling 100 buyers of each brand. Is this an example of a simple random sample?
Answer: • No, because every possible 400-buyer sample did not have an equal chance of being chosen.
Question:* Which of the following statements are true? 1. Categorical variables are the same as qualitative variables. 2. Categorical variables are the same as quantitative variables. 3. Quantitative variables can be continuous variables.
Answer: • 1 and 3 only
Question:* Suppose c is a constant number. Calculate var(c).
Answer: • 0
Question:* The variable X is the value of an uneven dice after one roll. It produced the following probability distribution P(X): P(1) = 0.05 P(2) = 0.28 P(3) = 0.12 P(4) = 0.23 P(5) = ? P(6) = ? What is the probability that X = 5 or X = 6?
Answer: • 0.32
Question:* Which of the following is a characteristic of an F-distribution?
Answer: • Right Skewed
Question:* Symbolism: What does the x-bar represent (without any other symbols) in statistics?
Answer: • Sample mean
Question:* _____ are collections of observations.
Answer: • Data
Question:* What is expected value?
Answer: • Sum of all the possible outcomes * the probability of occurrence
Question:* Experts rank athletic teams 1 through 10. This is an example of ______ data.
Answer: • ordinal
Question:* What is the probability of rolling a fair dice and getting an even number and flipping a fair coin getting a head?
Answer: • 0.25
Question:* Symbolism: What does the small sigma represent (without any other symbols) in statistics?
Answer: • Standard Deviation
Question:* What is true about these 5 numbers? -10, -5, 0, 1, 2
Answer: • The median is larger than the mean.
Question:* What is the skewness of a normal distribution?
Answer: • 0
Question:* You calculate the standard deviation of a data set and find that it is -1.23. From this you can determine which of the following is true?
Answer: • You made an arithmetic mistake because standard deviation cannot be negative.
Question:* Where would the outliers be if a distribution had a skewness of +50?
Answer: • Far right
Question:* What is the probability of rolling a fair dice and getting a 1 and flipping a fair coin getting a head?
Answer: • 1/12
Question:* How can you convert a variance to a standard deviation?
Answer: • Take the square root of the variance
Question:* Suppose a fair die is tossed twice. What is the probability of rolling two fours?
Answer: • 1/36
Question:* What is the difference between the mean and the median?
Answer: • Median is not affected by skewness of the distribution
Question:* Suppose E is an event in a sample space S with probability .3. What is the probability of the complement of E?
Answer: • .7
Question:* What is true about these 5 numbers? -2, -1, 0, 5, 10
Answer: • The mean is larger than the median.
Question:* Which of the following is not a measure of spread?
Answer: • Upper Quartile
Question:* The median grade on a midterm exam in a math class is 72. The teacher feels this is too low, so they award 10 extra points to every student in the class. What is the new median grade for the class?
Answer: • 82
Question:* The number of cars that went through a car wash during the noon hour over each of the past 8 days are the following: 5, 9, 2, 3, 3, 9, 8, 6 What is the range of this data?
Answer: • 7
Question:* A forestry researcher recorded many variables on the trees of a large forest. These variables include the height (in meters), the diameter (in centimeters), the species (pine, oak, etc.), and if the tree had Dutch Elm disease. In this study which variables that were recorded were quantitative?
Answer: • Only height and diameter.
Question:* Over the last 360 days of winter in Raleigh, NC (5 winters) we have had snow on 36 days. What is the probability that we will have snow on any random winter day this year?
Answer: • 0.1
Question:* Where would the outliers be if a distribution had a skewness of +1?
Answer: • Right
Question:* What power is used in the formula for variance?
Answer: • 2
Question:* Where would the outliers be if a distribution had a skewness of -50?
Answer: • Far left
Question:* Your college professor standardizes everyone's test scores. Your standardized score is -1.35. Which of the following statements is true?
Answer: • Your test score was below the average.
Question:* Discrete and continuous data are both forms of _______ data.
Answer: • quantitative
Question:* Bob is a high school basketball player, who is a 72% free throw shooter. Bob has missed his first four free throws of the game. What is the probability that Bob makes his fifth free throw?
Answer: • 72%
Question:* Using previous games to predict the score of a game is an example of ________ statistics.
Answer: • inferential
Question:* What is the skewness of a normal distribution?
Answer: • 0
Question:* Two coins are tossed, what is the probability that two heads are obtained?
Answer: • .25
Question:* What is the probability of rolling a fair dice and getting an even number?
Answer: • 1/2
Question:* The average grade on a midterm exam in a math class is 72. The teacher feels this is too low, so they award 10 extra points to every student in the class. What is the new average grade for the class?
Answer: • 82
Question:* Let A be a normal distribution with a mean of 3 and B be a normal distribution with a mean of 17. What is the mean of A+B?
Answer: • 20
Question:* Which of the following is NOT a characteristic of a Normal distribution?
Answer: • Right Skewed
Question:* You flip an unbiased coin 2 times - what is the probability of getting 2 heads?
Answer: • 25%
Question:* The, "null hypothesis," refers to
Answer: • that there is no relationship between two phenomena
Question:* True or false? Qualitative data is strictly numerical.
Answer: • False
Question:* Which of the following is a measure of spread?
Answer: • Range
Question:* The Square of the standard deviation is called
Answer: • Variance
Question:* What is the median of the following 5 numbers? 1, 2, 3, 4, 10
Answer: • 3
Question:* A normal distribution generally takes the form of _______.
Answer: • bell curve
Question:* Which of the following is quantitative data:
Answer: • Test scores for English class
Question:* What is the average of the following 5 numbers? 1, 2, 3, 4, 10
Answer: • 4
Question:* What is the value of the middle observation in a ordered set of numbers
Answer: • Median
Question:* A mean calculation is a part of _______ statistics.
Answer: • parametric
Question:* What is the mode of: 5, 10, 10, 15, 17?
Answer: • 10
Question:* The ______ describes the dispersion of a data set.
Answer: • standard deviation
Question:* Where would the outliers be if a distribution had a skewness of 0?
Answer: • No outliers
Question:* You flip an unbiased coin one time - what is the probability of getting tails?
Answer: • 50%
Question:* The difference between the highest and lowest scores is called the ______.
Answer: • range
Question:* What is the mean of: 5, 10, 15?
Answer: • 10
Question:* How is P(A|B) interpreted?
Answer: • The probability event A happens given that event B has happened
Question:* If a data set follows a normal distribution, approximately ___% of data falls within 1 standard deviation of the mean.
Answer: • 68%
Question:* Which plot is best use to display the relationship between a continuous dependent variable against a continuous independent variable
Answer: • Scatter plot
Question:* The variable X is the value of an uneven dice after one roll. It produced the following probability distribution P(X): P(1) = 0.05 P(2) = 0.28 P(3) = 0.12 P(4) = 0.23 P(5) = ? P(6) = ? What is the probability that X = 2 or X = 3?
Answer: • 0.4
Question:* The average price of a car in a used car lot is $18,000. These prices are Normally distributed with a standard deviation of $3,000. What is the probability that any random car is below $18,000?
Answer: • 50%
Question:* How do you calculate the Z-Score?
Answer: • = (observation - sample mean) / standard deviation
Question:* A ______ is a numerical characteristic of a population
Answer: • parameter
Question:* How can you convert a standard deviation to a variance?
Answer: • Square the standard deviation
Question:* What is the median of the following 5 numbers? 10, 2, 4, 3, 1
Answer: • 3
Question:* In a probability distribution, the second central moment can be another term for which of the following?
Answer: • Variance
Question:* Interpret an R-squared coefficient of .6 for a simple linear regression.
Answer: • 60% of the variability in our dependent variable can be explained by our independent variable.
Question:* Which one of these variables is a continuous random variable?
Answer: • The time it takes a randomly selected student to complete an exam.
Question:* What is the mean of a standard normal distribution?
Answer: • 0
Question:* Which of the following is an example of mutually exclusive events?
Answer: • Being late to a meeting and being early to the same meeting
Question:* When does a Type I error occur?
Answer: • You reject the null hypothesis when it is true
Question:* The probability of a discrete value in a continuous distribution is equal to __?
Answer: • 0
Question:* Which one of these variables is a binomial random variable?
Answer: • number of women taller than 68 inches in a random sample of 5 women
Question:* _____ data is an example of nonmetric data.
Answer: • Ordinal
Question:* What is derived from the second moment of distribution?
Answer: • Variance
Question:* What is the formula for the variance of a population?
Answer: • SUM(((observation - sample mean)^2) / Number of observations)
Question:* Suppose E and F are mutually exclusive events in a sample space S with probabilities .4 and .3 respectively. What is the probability of their union?
Answer: • .7
Question:* A bag contains 4 balls (2 red and 2 blue). You pull out one ball at a time without replacement. What is the probability that the fourth ball chosen is a red ball?
Answer: • 1/2
Question:* Which of the following would be appropriate for a z-test?
Answer: • Determining whether the life expectancy of women in a population is statistically different from that of men
Question:* Which of the following statements are true about confidence intervals for means? 1. The center of the confidence interval is always 0. 2. The bigger the confidence interval, the smaller the margin of error. 3. The bigger your sample, the smaller the margin of error.
Answer: • 3 only
Question:* The center line inside a box plot typically represents the _____ in any instance.
Answer: • Median of the distribution
Question:* Suppose you have generated this model to predict income: Income = 10 + .5(Years of Education), units are in thousands, ie 10.5 = $10,500. Interpret Beta1.
Answer: • For every additional year of education, income is expected to increase by $500.
Question:* A manager of a large bank wants to compute the average interest rates across all bonds that the bank invests in. The manager randomly sampled 127 bonds that the bank invests in and calculated the average interest rate over the past year of the sample was 2.47%. What is the parameter of interest in this study?
Answer: • The average interest rate of all bonds that the bank invests in.
Question:* What is the first moment of distribution?
Answer: • Mean
Question:* The preseason odds that the Hartford Whalers will win The Stanley Cup Championship are 1/4, and the odds are the same for the California Golden Seals. What is the probability that BOTH will win the championship?
Answer: • 0
Question:* If you have a hypothesis test with a significance level of 0.05 and a p-value of 0.01, what is the result of your hypothesis test?
Answer: • You reject the null hypothesis
Question:* Say 2 events satisfy the following equation: P(A intersect B) = P(A) x P(B). We say that events A and B are __.
Answer: • Independent
Question:* C(n,r) is equal to...
Answer: • n!/(r!(n-r)!)
Question:* Which of the following examples involves paired data?
Answer: • A group of 50 students had their blood pressures measured before and after watching a movie containing violence. The mean blood pressure before the movie was compared with the mean pressure after the movie.
Question:* The median grade on a midterm exam in a math class of 60 students is 85. The teacher gives an additional 5 bonus points to the 3 students who scored the highest on the exam. What is the new median grade for the class?
Answer: • 85
Question:* P(n,r) is equal to...
Answer: • n!/(n-r)!
Question:* Symbolism: What does the Greek letter mu represent (without any other symbols) in statistics?
Answer: • Population mean
Question:* In hypothesis testing, which of the following statements is always true?
Answer: • The P-value is a probability.
Question:* What is the cumulative probability at +1 standard deviation, for a random variable with normal distribution?
Answer: • 84.13%
Question:* A card is drawn randomly from an ordinary deck of playing cards. You win a prize if the card is a heart or the card is an ace. What is the probability that you will win the prize?
Answer: • 16/52
Question:* Which of the following is A test of normality?
Answer: • Kolmogrov-Smirnov Test of Normality
Question:* When do you fail to reject the null hypothesis?
Answer: • P-Value is > alpha (level of significance)
Question:* Find the z-score: mean = 6, standard dev. = 2, observation = 7
Answer: • .5
Question:* P(A)*P(B)=P(A and B) What can you conclude about A and B?
Answer: • They are independent.
Question:* What is derived from the third moment of distribution?
Answer: • Skewness
Question:* For a random variable X, E[X]=3 and E[X^2]=14. Var[X]=?
Answer: • 5
Question:* Suppose E and F are events in a sample space S. Suppose further that E has probability .2, F has probability .6, and the intersection of E and F has probability .1. What is the probability of the union of E and F?
Answer: • .7
Question:* The variance of X is 15. Y=X+5. What is the Variance of Y?
Answer: • 15
Question:* What power is used in the formula for skewness?
Answer: • 3
Question:* What are the characteristics of the f-distribution.
Answer: • It is skewed to the right, and we can only use it to perform one-tailed tests.
Question:* Suppose A is always 3. Var(B)=4. What is Var(A+B)?
Answer: • 4
Question:* Which of the following is NOT a commonly used estimator in determining the parameters of an unknown probability density function?
Answer: • Fourier transform
Question:* Suppose E and F are mutually exclusive events in a sample space S. Suppose further that E has probability .3 and F has probability .4. What is the probability of the intersection of E and F?
Answer: • 0
Question:* What is the kurtosis of a normal distribution?
Answer: • 3
Question:* Where would the outliers be if a distribution had a skewness of -1?
Answer: • Left
Question:* Suppose E and F are events in a sample space S. Suppose further that E has probability .8 and F has probability .9. What is the largest possible value for the probability of the intersection of E and F?
Answer: • .8
Question:* For an airline, many times small cities have limited flights that go into their airports. To get a flight to Columbia, SC you must go through one of three cities: Raleigh, NC, Atlanta, GA, or Charlotte, NC. Two customers from Orlando, FL are trying to get to Columbia, SC with only one stop (one of the three above mentioned cities). Assume that they are equally likely to go through any of the above cities. What is the probability neither of the customers fly through Charlotte, NC?
Answer: • 4/9
Question:* C(n,0) = C(n,n)
Answer: • True
Question:* Which of the following would be appropriate for ANOVA?
Answer: • Determining which of several training programs yields the highest mean performance score on the exit exam
Question:* What is the probability that two six-sided dice will roll the same number?
Answer: • 1/6
Question:* What is the expected value of rolling an unbiased die (6 sided)?
Answer: • 3.5
Question:* If I tossed a fair coin 3 times, what is the probability of it landing on tails only once?
Answer: • 3/8
Question:* What is the probability of rolling a seven on two six-sided dice?
Answer: • 1/6
Question:* Let X follow a Poisson distribution with a rate parameter of 7. What is Var(X)?
Answer: • 7
Question:* What is a Type II error?
Answer: • Failure to reject the null hypothesis when it is false
Question:* What is homoskedastic?
Answer: • The adjustment factor doesn't change (e.g. epsilon)
Question:* What is synonymous with the coefficient of determination?
Answer: • R-Squared
Question:* In a multiple regression model, what is the best way to test the joint significance of the independent variables?
Answer: • Nested F-test
Question:* How do you calculate the standard error of the mean? (obs. = observations, sqrt = Square Root)
Answer: • Standard deviation/ sqrt(number of obs.)
Question:* What is synonymous with the correlation coefficient?
Answer: • R
Question:* For an airline, many times small cities have limited flights that go into their airports. To get a flight to Columbia, SC you must go through one of three cities: Raleigh, NC, Atlanta, GA, or Charlotte, NC. Two customers from Orlando, FL are trying to get to Columbia, SC with only one stop (one of the three above mentioned cities). Assume that they are equally likely to go through any of the above cities. What is the probability one of the customers fly through Charlotte, NC, while the other does not fly through Charlotte, NC?
Answer: • 4/9
Question:* Chi-square is used predominantly in _______ statistics.
Answer: • non-parametric
Question:* The variance of X is 3. Y=3X. What is the variance of Y?
Answer: • 9
Question:* Which should you use to analyze a continuous dependent variable against a categorical independent variable?
Answer: • ANOVA
Question:* Which statistic is not a measure of effect size?
Answer: • F-statistic
Question:* What formula is used to determine the probability of a series of outcomes WITH replacement?
Answer: • Hypergeometric
Question:* A survey was conducted to find the average weight of students living in the dorms or a university. To help improve the accuracy of the study, an equal number of students were randomly selected from each dorm for the sample. This sample is an example of what?
Answer: • Simple Random Sample
Question:* What does R^2 (R-Squared) calculate?
Answer: • The closeness of a regression to the underlying data
Question:* Which of the following numbers (measures of kurtosis of a distribution) would represent a platykurtic distribution?
Answer: • 2
Question:* What is the coefficient of variation?
Answer: • Normalized measure of dispersion of a probability distribution
Question:* A coin is tossed three times. What is the probability that it lands on heads exactly one time?
Answer: • 0.375
Question:* Suppose E and F are independent events in a sample space S. Suppose further that E has probability .3 and F has probability .4. What is the probability of the intersection of E and F?
Answer: • .12
Question:* The variance of X is 5 and the variance of Y is 8. What is the variance of X+Y?
Answer: • Not enough information.
Question:* Which of the assumptions is not one of the assumptions for creating a linear regression model (ie. Gauss-Markov Assumptions)?
Answer: • The residuals must have a variance that depends on the values in the explanatory variable.
Question:* P(X|Y)=.5 P(X)=.2 P(Y)=.4 What is P(X and Y),
Answer: • .2
Question:* What power is used in the formula for kurtosis?
Answer: • 4
Question:* A card is drawn randomly from a deck of ordinary playing cards. You win $10 if the card is a spade or an ace. What is the probability that you will win money from playing the game once?
Answer: • 4/13
Question:* What is another form of expressing beta1 in a simple linear regression? y=dependent variable x=independent variable
Answer: • cov(xy)/var(x)
Question:* Which of the following numbers (measures of kurtosis of a distribution) would represent a leptokurtic distribution?
Answer: • 4
Question:* Which of the following would be appropriate for a t-test?
Answer: • Determining if a group of people who slept 4 hours before a test will score lower than a group of people who slept 8 hours before a test.
Question:* Which of these linear regression models is quadratic?
Answer: • Y = B0 + B1X1 + B2(X1)^2
Question:* What is the probability that a coin will land on the same side when flipped twice?
Answer: • .5
Question:* Event A and Event B are independent and mutually exclusive. True or False: The probability of A must be 0 or the probability of B must be 0.
Answer: • True
Question:* Suppose E and F are events in a sample space S. Suppose further that E has probability .3, F has probability .4, and the intersection of E and F has probability .2. Find the probability of the intersection of E and (the complement of F).
Answer: • .1
Question:* Suppose E and F are events in a sample space S. Suppose further that E has probability .8 and F has probability .9. What is the smallest possible value for the probability of the intersection of E and F?
Answer: • .7
Question:* Suppose X and Y are independent random variables. The variance of X is equal to 16; and the variance of Y is equal to 9. Let Z = X - Y. What is the standard deviation of Z?
Answer: • 5
Question:* P(A|B)=.6 P(A)=.3 P(B)=.4 What is P(B|A)?
Answer: • .8
Question:* What is the probability of drawing an Ace from a deck of cards that includes the two Jokers?
Answer: • 2/27
Question:* What is the cumulative probability at -1 standard deviation for a normal distribution?
Answer: • 15.87%
Question:* What is the formula for the Pearsonian Coefficient of Skewness?
Answer: • 3*(population mean - population mode) / Standard deviation
Question:* Which of the following is NOT essential for multiple regression modeling?
Answer: • The sample population must be derived from a normally distributed population.
Question:* Suppose E and F are events in a sample space S. Suppose further that E has probability .5, F has probability .6, and the intersection of E and F has probability .2. Find the probability of the union of E and (the complement of F).
Answer: • .6
Question:* Suppose E and F are independent events in a sample space S. Suppose further that E has probability .3 and F has probability .4. What is the probability of the union of E and F?
Answer: • .58
Question:* Is it true that nCr = nC(n-r) ?
Answer: • yes
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