Question: What is a bimodal distribution? What should

> a. What additional criterion must be satisfied for a one sided confidence interval to be valid (in addition to the two assumptions needed for a two-sided confidence interval)? b. If in doubt, should you use a one-sided or a two sided confidence interval?

> a. Why must a one-sided confidence interval always include the sample average? b. Must a one-sided confidence interval always include the population mean?

> Test to see if the population mean age for training level A differs from that for levels B and C combined.

> a. What is the central limit theorem? b. Does the central limit theorem specify that individual cases follow a normal distribution? c. How do you interpret the idea that the average has a normal distribution? d. What is the mean of a sum of independent o

> a. What is an estimator? b. What is an estimate? c. A sample standard deviation is found to be 13.8. Is this number an estimator or an estimate of the population standard deviation? d. What is the error of estimation? When you estimate an unknown number,

> a. What is a pilot study? b. What can go wrong if you do not do a pilot study?

> a. What is a random sample? b. Why is a random sample approximately representative? c. What is the difference between a random sample selected with and one selected without replacement? d. What is a table of random digits? How is it used in sample select

> a. What is a representative sample? b. What is a biased sample? c. How can a representative sample be chosen?

> a. What is a systematic sample? b. What are the main problems with systematic samples? c. Why is there no reliable standard error available for use with a sample average computed from a systematic sample?

> a. What is a stratified random sample? b. What are the benefits of stratification? c. When is stratification most likely to be helpful?

> a. What is the finite-population correction factor? b. What is the adjusted standard error? c. What is an idealized population? d. In what way are your results more limited if you use the finite-population correction factor than if you do not?

> a. What is the standard error of a statistic? b. In what way does the standard error indicate the quality of the information provided by an estimate? c. What typically happens to the standard error as the sample size, n, increases?

> a. What is a population? b. What is a sample? Why is sampling useful? c. What is a census? Would you always want to do a census if you had the resources?

> Now examine the effect of gender on annual salary, with and without adjusting for age and experience. a. Find the average annual salary for men and for women and compare them. b. Using a two-sided test at the 5% level, test whether men are paid significa

> a. What kinds of situations give rise to an exponential distribution? b. What is meant by the fact that an exponential random variable has no memory? c. Can the standard normal probability table be used to find probabilities for an exponential distributi

> a. What kinds of situations give rise to a Poisson distribution? b. Is the Poisson a discrete or a continuous distribution? c. What is the standard deviation of a Poisson distribution? d. How do you find probabilities for a Poisson distribution if the me

> a. What is a normal distribution? b. Identify all of the different possible normal distributions. c. What does the area under the normal curve represent? d. What is the standard normal distribution? What is it used for? e. What numbers are found in the s

> a. What is a factorial? b. Find 3!, 0!, and 15!. c. What is a binomial coefficient? What does it represent in the formula for a binomial probability? d. Find the binomial coefficient “8 choose 5.”

> For a binomial distribution: a. Why do not you just construct the probability tree to find the probabilities? b. How do you find the mean and the standard deviation? c. How do you find the probability that X is equal to some number? d. How do you find th

> a. How do you tell if a random variable has a binomial distribution? b. What is a binomial proportion? c. What are n, π, X, and p?

> a. What is the probability distribution of a discrete random variable? b. How do you find the mean of a discrete random variable? How do you interpret the result? c. How do you find the standard deviation of a discrete random variable? How do you interpr

> a. What is a discrete random variable? b. What is a continuous random variable? c. Give an example of a discrete random variable that is continuous for practical purposes.

> a. What is a random variable? b. What is the difference between a random variable and a number?

> a. Name the three main sources of probability numbers. b. What is the equally likely rule? c. Are you allowed to use someone’s guess as a probability number? d. What is the difference between a Bayesian and a frequentist analysis?

> Suppose males and females are equally likely and that the number of each gender follows a binomial distribution. (Note that the database contains observations of random variables, not the random variables themselves.) a. Find n and π for the binomial dis

> a. What is the relative frequency of an event? b. How is the relative frequency different from the probability of an event? c. What is the law of large numbers?

> a. What is a probability? b. Which of the following has a probability number: a random experiment, a sample space, or an event? c. If a random experiment is to be run just once, how can you interpret an event with a probability of 0.06?

> What is a Venn diagram?

> a. What is a probability tree? b. What are the four rules for probability trees?

> a. What is the interpretation of independence of two events? b. How can you tell whether two events are independent or not? c. Under what conditions can two mutually exclusive events be independent?

> a. What is the interpretation of conditional probability in terms of new information? b. Is the conditional probability of A given B, always the same number as the conditional probability of B given A? c. How can you find the conditional probability from

> a. What is the union of two events? b. What is the probability of “one event or another” if you know, (1) Their probabilities and the probability of “one event and the other”? (2) That they are mutually exclusive?

> a. What is the intersection of two events? b. What is the probability of “one event and another” if you know (1) Their probabilities and the probability of “one event or the other”? (2) Their probabilities and that they are independent? (3) That they are

> a. What is the range? b. What are the measurement units of the range? c. For what purposes is the range useful? d. Is the range a very useful statistical measure of variability? Why or why not?

> How would your answers to question 6 change if the data were not normally distributed? Data from question 6: If your data set is normally distributed, what proportion of the individuals do you expect to find: a. Within one standard deviation from the a

> Continue using predictions of annual salary based on age and experience. a.* Find the predicted annual salary and prediction error for employee 33 and compare the result to the actual annual salary. b. Find the predicted annual salary and prediction erro

> Would the average-based procedure they are currently using ordinarily be a good method? Or is it fundamentally flawed? Justify your answers.

> a. What is the variance? b. What are the measurement units of the variance? c. Which is the more easily interpreted variability measure, the standard deviation or the variance? Why? d. Once you know the standard deviation, does the variance provide any a

> a. What is the standard deviation? b. What does the standard deviation tell you about the relationship between individual data values and the average? c. What are the measurement units of the standard deviation? d. What is the difference between the samp

> When each data value is multiplied by a fixed number, what happens to a. The average, median, and mode? b. The standard deviation and range? c. The coefficient of variation?

> What is a weighted average? When should it be used instead of a simple average?

> What is the average? Interpret it in terms of the total of all values in the data set.

> What is an outlier? How do you decide whether a data point is an outlier or not?

> What is a percentile? In particular, is it a percentage (e.g., 23%), or is it specified in the same units as the data (e.g., $35.62)?

> How do you usually define the mode for a quantitative data set? Why is this definition ambiguous?

> Consider the cumulative distribution function: a. What is it? b. How is it drawn? c. What is it used for? d. How is it related to the histogram and box plot?

> What kinds of trouble do outliers cause?

> View each column as a collection of independent observations of a random variable. a. In each case, what kind of variable is represented, continuous or discrete? Why? b.* Consider the event “annual salary is above $40,000.” Find the value of the binomial

> Why is it important in a report to explain how you dealt with an outlier?

> Why is it important to identify the source of funding when evaluating the results of a statistical study?

> Distinguish between primary and secondary data.

> Differentiate between probability and statistics.

> Differentiate between time-series data and cross sectional data.

> What is the difference between ordinal and nominal qualitative data?

> What is the main problem with skewness? How can it be solved in some cases?

> What is the difference between discrete and continuous quantitative variables?

> What is the difference between a histogram and a bar chart?

> Answer the parts of exercise 1 using experience in place of annual salary. Data from exercise 1: Break down the annual salaries into three groups according to training level (A, B, or C). a.* Draw box plots to compare these three groups. Comment on wha

> What can you gain by exploring data in addition to looking at summary results from an automated analysis?

> Why is random sampling a good method to use for selecting items for study?

> What general questions can be answered by analysis of a. Univariate data? b. Bivariate data? c. Multivariate data?

> What are the five basic ways in which data sets can be classified?

> List and briefly describe the different methods for summarizing a data set.

> Consider the quality of cars, as measured by the number of cars requiring extra work after assembly, in each day’s production for 15 days: 30, 34, 9, 14, 28, 9, 23, 0, 5, 23, 25, 7, 0, 3, 24 a. Find the average number of defects per day. b. Find the medi

> Your firm is considering the introduction of a new toothpaste. At a strategy session, it is agreed that a marketing study will be successful with probability 0.65. It is also agreed that the probability of a successful product launch is 0.40. However, gi

> You are operations manager for a plant that produces copy machines. At the end of the day tomorrow, you will find out how many machines were produced and, of these, how many are defective. a. Describe the random experiment identified here. b. What is the

> The coming year is expected to be a good one with probability0.70. Given that it is a good year, you expect that a dividend will be declared with probability 0.90. However, if it is not a good year, then a dividend will occur with probability 0.20. a. Dr

> There are two locations in town (north and south) under consideration for a new restaurant, but only one location will actually become available. If it is built in the north, the restaurant stands a 90% chance of successfully surviving its first year. Ho

> Answer the parts of exercise 1 using age in place of annual salary. Data from exercise 1: Break down the annual salaries into three groups according to training level (A, B, or C). a.* Draw box plots to compare these three groups. Comment on what you s

> Your firm is planning a new style of advertising and figures that the probability of increasing the number of customers is 0.63, while the probability of increasing sales is 0.55. The probability of increasing sales given an increase in the number of cus

> It is currently difficult to hire in the technology sector. Your company believes that the chances of successfully hiringthisyearare0.13.Giventhatyourcompanyissuccessful in hiring, the chances of finishing the project on time are 0.78, but if hiring is n

> A repair shop has two technicians with different levels of training. The technician with advanced training is able to fix problems 92% of the time, while the other has a success rate of 80%. Assume you have a 30% chance of obtaining the technician with a

> The human resources department of a company is considering using a screening test as part of the hiring process for new employees and is analyzing the results of a recent study. It was found that 63% of applicants score high on the test, but only 79% of

> Your company maintains a database within formation on your customers, and you are interested in analyzing patterns observed over the past quarter. In particular, 23% of customers in the database placed new orders within this period. However, for those cu

> Two events are mutually exclusive, one with probability 0.38 and the other with probability 0.54. a. Find the conditional probability that the first event happens given that the second event happens. b. Find the probability of the union of these two even

> Your firm has classified orders as either large or small in dollar amounts and as either light or heavy in shipping weight. In the recent past, 28% of orders have been large dollar amounts, 13% of orders have been heavy, and 10% of orders have been large

> The probability of getting a big order currently under negotiation is 0.32. The probability of losing money this quarter is 0.54. a. Assume that these are mutually exclusive events. Find the probability of getting the order or losing money this quarter.

> As a stock market analyst for a major brokerage house, you are responsible for knowing everything about the automotive companies. In particular, Ford is scheduled to release its net earnings for the past quarter soon, and you do not know what that number

> Based on a demand analysis forecast, a factory plans to produce 80,000 video game cartridges this quarter, on average, with an estimated uncertainty of 25,000 cartridges as the standard deviation. The fixed costs for this equipment are $72,000 per quarte

> Break down the annual salaries into three groups according to training level (A, B, or C). a.* Draw box plots to compare these three groups. Comment on what you see. b.* Find the average for each training level, and comment. c.* Find the between-sample a

> Repeat problem 6 with the extreme outlier omitted, and write a paragraph comparing the results with and without the outlier. Data from problem 6: Consider the number of executives for all Seattle corporations with 500 or more employees 19: 12, 15, 5, 1

> Consider the number of executives for all Seattle corporations with 500 or more employees 19: 12, 15, 5, 16, 7, 18, 15, 12, 4, 3, 22, 4, 12, 4, 6, 8, 4, 5, 6, 4, 22, 10, 11, 4, 7, 6, 10, 10, 7, 8, 26, 9, 11, 41, 4, 16, 10, 11, 12, 8, 5, 9, 18, 6, 5 a. Fi

> Consider the assets of stock mutual funds, as shown in Table 5.5.3. Answer the parts of the previous problem using the column of assets instead of the rates of return. Table 5.5.3: TABLE 5.5.3 Natural Resources Mutual Funds: Rates of Return (12 mo

> Using the data from Table 2.6.7 of Chapter 2 for the 30 Dow Jones Industrial companies percent changes since January 2015: a. Find the standard deviation of the percent change. b. Find the range of the percent change. Table 2.6.7: TABLE 2.6.7 Closi

> How much variability is the rein loan fees for home mortgages? Find and interpret the standard deviation, range, and coefficient of variation for the data in Table 4.3.8 of Chapter 4. Table 4.3.8: TABLE 4.3.8 Home Mortgage Loan Fees for Dallas, TX

> Use the data set from problem 21 of Chapter 3 on poor quality in the production of electric motors. a. Find the standard deviation and range to summarize the typical batch-to-batch variability in quality of production. b. Remove the two outliers and re c

> Using the data from Table 3.8.4 in Chapter 3 for the market values of the portfolio investments of College Retirement Equities Growth Fund (CREF) in the media sector: a. Find the standard deviation of portfolio value for these firms’ st

> For the municipal bond yields of Table 3.8.1 in Chapter 3: a. Find the standard deviation of the yield. b. Find the range. c. Find the coefficient of variation. d. Use these summaries to describe the extent of variability among these yields. Table 3.8.1

> For the international goods and services tax data of Table 5.5.10, which shows these taxes as a percentage of GDP (gross domestic product, a measure of total national economic activity) and as a percentage of revenue: a. Draw a box plot for each variable

> Different countries have different taxation strategies: Some tax income more heavily than others, while others concentrate on goods and services taxes. Consider the relative size of goods and services taxes for selected countries’ inter

> Write a three- to five-page report summarizing the relationship between gender and salary for these employees. Be sure to discuss the results of the following statistical analyses: (a) a two-sample t-test of male salaries against female salaries and (b)

> Consider the return on equity, expressed like an interest rate in percentage points per year, for a sample of companies: 5.5, 10.6, 19.0, 24.5, 6.6, 26.8, 6.2, 2.4, 28.3, 2.3 a. Find the average and standard deviation of the return on equity. b. Interpre

> Samples from the mine show the following percentages of gold: 1.1, 0.3, 1.5, 0.4, 0.8, 2.2, 0.7, 1.4, 0.2, 4.5, 0.2, 0.8 a. Compute and interpret the sample standard deviation. b. Compute and interpret the coefficient of variation. c. Which data value ha

> Here are first-year sales (in thousands) for some recent new product introductions that are similar to one you are considering. 10, 12, 16, 47, 39, 22, 10, 29 a. Find the average and standard deviation. Interpret the standard deviation. b. After you went

> Consider the following productivity measures (on a scale from 0 to 100) for a population of employees: 85.7, 78.1, 69.1, 73.3, 86.8, 72.4, 67.5, 76.8, 80.2, 70.0 a. Find the average productivity. b. Find and interpret the standard deviation of productivi

> Consider the annualized stock return over the decade from 2000 to 2010, July to July, expressed as an annual interest rate in percentage points per year, for major pharmaceutical companies as shown in Table 5.5.2. For these top firms in this industry gro

> Here are rates of return for a sample of recent on-site service contracts: 78.9%, 22.5%, 5.2%, 997.3%, 20.7%, 13.5%, 429.7%, 88.4%, 52.1%, 960.1%, 38.8%, 70.9%, 73.3%, 47.0%, 1.5%, 23.9%, 35.6%, 62.0%, 75.7%, 14.0%, 81.2%, 46.9%, 135.1%, 34.6%, 85.3%, 73

> Consider the variability in traffic congestion in Table 5.5.5 for northeastern and for southwestern cities. a. Compare population variability of these two groups of cities. In particular, which group shows more variability in congestion from city to city

> We have all been stopped by traffic at times and have had to sit there while freeway traffic has slowed to a crawl. If you have someone with you (or some good music), the experience may be easier to put up with, but what does traffic congestion cost soci

> You have been trying to control the weight of a chocolate and peanut butter candy bar by intervening in the production process. Table 5.5.4 shows the weights of two representative samples of candy bars from the day’s production, one tak