Practice exam questions with the book Statistics for Business and Economics - Newbold, Carlson & Thorne. Practice material donated to JoHo WorldSupporter, unclear to which edition of the book the questions relate

Questions - Chapter 1

1. What is the difference between population and sample?
2. What is the difference between simple random sampling and systematic sampling?
3. What is the difference between a parameter and a statistic?
4. What are non-sampling errors?
5. What is the difference between descriptive statistics and inferential statistics?
6. There are two forms of numeric variables, which ones?
7. What is the difference between qualitative and quantitative data?
8. What levels of measurement are used for qualitative data?
9. What levels of measurement are used for quantitative data?
10. Which tables and graphs are mainly used for nominal level of measurement?
11. Which graphs are mainly used to describe numerical variables?

Questions - Chapter 2

1. What are numerical measures and what questions do they answer?
2. What measures are used for categorical data?
3. What measures are used for numerical data?
4. How do you know which way the skewness of the distribution is?
5. How do you know whether the distribution is symmetrical?
6. What is the five-number summary?
7. How do you calculate the interquartile range?
8. Which graph shows the shape of the distribution in terms of the five-number summary?
9. How do you calculate the variance?
10. What is the difference between Chebyshey’s theorem and the z-score?
11. What have covariance and correlation coefficient in common?

Questions - Chapter 3

1. What are basic outcomes and what do they have to do with the sample space?
2. When are the events collectively exhaustive?
3. What is the difference between permutations and combinations?
4. What is the difference between classical probability and subjective probability?
5. What are the five rules of chance?
6. What are the possible consequences when multiple measurements on the same sample?

Questions - Chapter 4

1. What are the required properties of probability distribution for discrete random variables?
2. What is the expected value of a discrete random variable X?
3. How do we calculate the standard deviation?
4. What are the characteristics of a binomial probability distribution?
5. What are the possible outcomes of a binomial distribution (Bernoulli)?
6. What are the characteristics of joint probability distributions of discrete random variables?
7. How do you know whether the joint distributed random variables X and Y are independent?
8. What is a portfolio analysis?

Questions - Chapter 5

1. What is the probability that a continuous random variable falls in a given range.?
2. What are the properties of a probability density function?
3. How does the probability density function look at a normal distribution?
4. What is the notation of the normal distribution?
5. What is the formula for a normally distributed random variable, and Z?

Questions - Chapter 6

1. Why do we often use a sample?
2. What does the central limit theorem say?
3. What is the acceptance interval?
4. What is the sample proportion?

Questions - Chapter 7

1. What is the difference between an estimator and an estimate?
2. What is the bias of an unbiased estimator?
3. What is the most efficient estimator?
4. How is the confidence interval of an estimate determined?
5. How are the limits of a confidence interval indicated??
6. In what way could we reduce the margin of error??
7. When is the student’s t distribution used?

Questions - Chapter 8

1. When are samples dependent?
2. What does d̄ stand for?
3. What does it mean when the result between two drug µ_x- µ_y is positive?
4. What variable do you use when the population variance is unknown?
5. How are these observed variations used in the sample interval formula if considered equal?
6. When may you use the difference between two population proportions?
7. What is the interval formula of the difference between two population proportions?

Questions - Chapter 9

1. What is the difference between the null hypothesis and the alternative hypothesis? 
2. When is the hypothesis one-sided and when is it two-sided?
3. What are the two possible errors in hypothesis testing?
4. What happens if a result falls in the rejection region?
5. When do you reject the null hypothesis based on the p-value?
6. How do you determine the strength of a test?

Questions - Chapter 10

1. How do we formulate the hypothesis when testing the differences between two normal population means (two-sided)?
2. What is the difference in t or z at a one-sided and two-sided test?
3. With which distribution do we test the equality of the variations between two normally distributed populations?
4. How do we formulate the hypothesis when testing the equality of the variations between two normally distributed populations?
5. What are the key assumptions of hypothesis testing based on?

Questions - Chapter 11

1. What do b1 and b0 mean in a least squares regression line?
2. What components are in the analysis of variance?
3. What does the coefficient of determination say about the regression?
4. Which two quantities determine the variance of the slope coefficient?
5. When can we use regression models in the prediction of the dependent variable?
6. What is the result of a wider interval?
7. Which three volumes affect the prediction and confidence intervals and in what way?
8. What is the difference between diversifiable risk and non diversifiable risk?
9. Name three examples of diversifiable risk.
10. How could the diversifiable risk be controlled?
11. What does the beta coefficient say?
12. What does it mean when the beta coefficient is 1?
13. How do you know the return on a company reacts violently on the market?
14. What are the components of the required return on an investment?
15. What are extreme points?
16. What are outlier points?

Questions - Chapter 14

1. For what do we use a goodness-of-fit test?
2. Which variable is used in a goodness-of-fit test?
3. What chance does H0 describe in a goodness-of-fit test?
4. How do you calculate the degrees of freedom of a chi-squared random variable when the population parameters are estimated?
5. What is being tested with the Jarque-Bera test?
6. What are the two parts of a Jarque-Bera test?
7. How do we formulate the null hypothesis at a chi-squared random variable for contingency table?
8. What can we calculate with a sign test?
9. How do we formulate the null hypothesis of a sign test?
10. What is a disadvantage of the sign test?
11. What method can be used to associate the magnitude of the difference in the test?
12. When does the Mann-Whitney U test approximate the normal distribution?
13. What is the Spearman rank correlation coefficient?
14. What is the null hypothesis of a runs test?

Answers - Chapter 1

1. The population is the complete set of items that interest an investigator. A sample is an observed subset of a population.
2. Simple random sampling is a procedure where objects are randomly selected. Systematic sampling involves the selection of every jth item in the population.
3. A parameter describes a specific characteristic of the population. A statistic describes a specific characteristic of a sample.
4. The population actually sampled is not the relevant one. Participants can give inaccurate or dishonest answers. Participants give no response.
5. Descriptive is to to summarize and process data. Inferential focuses on using the data.
6. Discrete variables and continuous variables.
7. With qualitative data, there is no measurable difference in meaning between the numbers. With quantitative there is a measurable meaning to the difference.
8. Nominal and ordinal.
9. Interval and ratio.
10. Bar chart, cross table, pie chart, pareto diagram.
11. Frequency distribution, histogram, ogive, stem-and-leaf display, scatter plot.

Answers - Chapter 2

1. The mean, median and mode. On questions about the location of the center of a data set.
2. Median or mode
3. Mean or median
4. Skewness is positive if the distribution is skewed to the right, negative for distributions skewed to the left.
5. If the skewness is zero and the distribution is bell-shaped.
6. Refers to the five descriptive measures: minimum, first quartile, median, third quartile, and maximum.
7. The third quartile – the first quartile: Q3-Q1.
8. Box-and-whisker plot (boxplot)
9. The sum of the squared differences between each observation and the population mean divided by the sample or population size.
10. Chebyshey’s theorem: The number of observations in a sample within k standard deviations of the mean.
    Z-score: A value that indicates the number of standard deviations a value is from the mean.
11. Both of them measure the direction of a linear relationship between two variables. The correlation coefficient also indicates the strength of the relationship between two variables.

Answers - Chapter 3

1. Basic outcomes are all possible outcomes of a random experiment. All basic outcomes together are called the sample space. The part of the basic results of interest is called an event.
2. If the union of several events covers the entire sample space.
3. With permutations the order of objects is important, with combinations this is not of interest.
4. Classical: proportion of times that an event will occur, assuming that all outcomes in a sample space are equally likely to occur.
   Subjective probability: expresses an individual’s degree of belief about the chance that an event will occur.
5. Complement rule, addition rule, conditional probability, multiplication rule, statistical independence.
6. Joint probability, marginal probability, conditional probability, over involvement ratios.

Answers - Chapter 4

1. F(x0) is between 0 and 1 for each x0, the sum of the individual probabilities is 1.
2. The mean, µ
3. The positive square root of the variance.
4. Several trials, each of which has only two outcomes. The probability of the outcome is the same for each trial. The probability of the outcome on one trial does not affect the probability on other trials.
5. Success and failure.
6. P(x,y) is between 0 and 1. The sum of the joint probabilities P(x,y) over all possible pairs of values must be 1.
7. If their joint probability distribution is the product of their marginal probability distributions.
8. The linear combination of the mean values of the stocks in the portfolio.

Answers - Chapter 5

1. P(a < X < b) = F(b) - F(a) 
2. F(x) > 0 for all values of x. The area under the probability density function over all values of the random variable is equal to 1.0. The probability that X lies between a and b is the area under the probability density function between these points. The cumulative distribution function is the area under the probability density function up to x₀.
3. A symmetrical bell-shaped curve with the average as the center.
4. X ~ N(µ,σ²)
5. Z = (X-µ)/σ

Answers - Chapter 6

1. It is very difficult and expensive to measure each item in a population.
2. If n is large, the central limit theorem says that the distribution of Z approaches the standard normal distribution.
3. An interval in which a sample mean has a high probability of occurring.
4. The proportion of the population members that have a characteristic of interest.

Answers - Chapter 7

1. An estimator is a random variable that depends on the sample information. An estimate is a specific value of the random variable.
2. Zero
3. The unbiased estimator with the smallest variance.
4. a<θ<b, with 100(1-α)%
5. Upper confidence limit and Lower confidence limit
6. By reducing the standard deviation, increasing the sample size or decreasing the confidence level.
7. If the population variance is unknown.

Answers - Chapter 8

1. If the values in one sample are influenced by the values in the other sample.
2. The average of the differences.
3. That X is more effective than Y.
4. The observed sample variations S²_x and S²_y
5. The pooled sample variance S²_p
6. For large samples.
7. (p̂_x - p̂_y) ± ME

Answers - Chapter 9

1. The null hypothesis is considered to be true. When the null hypothesis is rejected, the alternative hypothesis is regarded as the truth.
2. One-sided if alternative; larger or smaller than. Two-sided when alternative hypothesis; not equal to.
3. Type I error: rejecting a true null hypothesis
   Type II error: not rejecting a false null hypothesis
4. The null hypothesis is rejected.
5. When it is significant, the p-value is < 0.05.
6. By 1 - β

Answers - Chapter 10

1. H0: µ_x - µ_y = 0
   H1: µ_x - µ_y ≠ 0
2. In a two-tailed test, the alpha is divided by two.
3. With the F distribution
4. Ho: σ²_x = σ²_y
   H1: σ²_x ≠ σ²_y
5. The assumption that the underlying distribution is normal, or that the central limit theory is applicable.

Answers - Chapter 11

1. b1 represents the slope and b0 represents the intersection with the y-axis.
2. Sum of squares total, sum of squares error and sum of squares regression.
3. A higher value means a better regression.
4. The distance of the points on the regression line, and the total deviation of the X values of the average.
5. If the future value of the independent variable is given.
6. The wider the interval, the greater the uncertainty surrounding the point prediction.
7. The larger S²_e, the greater the prediction interval and the confidence interval.
   The larger the sample size n, the narrower the prediction interval and the confidence interval.
   The greater the dispersion, the more information, the more precise estimates.
8. Diversifiable risk is that risk associated with specific firms and industries.
   Non diversifiable risk is the risk associated with the entire economy.
9. Labor conflicts, new competition, consumer market changes.
10. By larger portfolio sizes and by including stocks whose returns have negative correlations.
11. How responsive the returns for a particular firm are to the overall market returns.
12. Then a company’s returns follow the market exactly.
13. If the beta is more than 1.
14. Risk-free rate, beta for investment and market return.
15. Points that have X values that deviate substantially from the X values of the other points.
16. Points that deviate substantially in the Y direction from the predicted value.

Answers - Chapter 14

1. To describe the population of nominal data.
2. The chi-square random variable
3. The probability that an observation falls into each category.
4. (K-m-1).
5. The normality of a distribution.
6. The skewness and kurtosis.
7. H0: there is no relationship between two characteristics in the population.
8. The probability that the difference is negative or positive.
9. Ho: P=0.5
10. That is only processes a limited part of the information, only the sign of difference.
11. The Wilcoxon Signed rank test.
12. When each sample contains at least 10 observations.
13. If x_i and y_i are each ranked in ascending order and the sample correlation of these ranks is calculated, the resulting coefficient is called the Spearman rank correlation coefficient.
14. H0: the series is random