BMAL 590 FOUNDATIONS OF QUANTATIVE RESEARCH TECHNIQUES AND STATISTICS

Review Questions 1. A company has developed a new smartphone whose average lifetime is unknown. In order to estimate this average, 200 smartphones are randomly selected from a large production line and tested; their average lifetime is found to be 5 years. The 200 smartphones represent a blank__________. o Sample 2. Which of the following is a measure of the reliability of a statistical inference? o A Significance Level 3. The process of using sample statistics to draw conclusions about population parameters is called blank__________. o doing inferential statistics 4. Which of the following statements involve descriptive statistics as opposed to inferential statistics? o The Alcohol, Tobacco and Firearms Department reported that Houston had 1,791 registered gun dealers in 1997. 5. A population of all college applicants exists who have taken the SAT exam in the United States in the last year. A parameter of the population are blank__________. o SAT Scores 6. Which of the following statements is true regarding the design of a good survey? o The questions should be kept as short as possible 7. Which method of data collection is involved when a researcher counts and records the number of students wearing backpacks on campus on a given day? o Direct observation 8. The manager of the customer service division of a major consumer electronics company is interested in determining whether the customers who have purchased a videocassette recorder over the past 12 months are satisfied with their products. If there are four different brands of videocassette recorders made by the company, the best sampling strategy would be to use a blank__________. o stratified random sample 9. Which of the following types of samples is almost always biased? o Self-selected samples 10._________ is an expected error based only on the observations limited to a sample taken from a population. o sampling error 11.Bayes's Law is used to compute blank__________. BMAL 590 FOUNDATIONS OF QUANTATIVE RESEARCH TECHNIQUES AND STATISTICS o posterior probabilities 12.The classical approach describes a probability blank_________. o in terms of the proportion of times that an event can be theoretically expected to occur 13.If a set of events includes all the possible outcomes of an experiment, these events are considered to be blank__________. o Exhaustive 14.Which of the following statements is not correct? o If event A does not occur, then its complement A' will also not occur. 15.The blank__________ can determine the union of two events such as event A and event B. o addition rule 16.The that allows us to draw conclusions about the population based strictly on sample data without having any knowledge about the distribution of the underlying population is blank___________. o the central limit theorem 17.Each of the following are characteristics of the sampling distribution of the mean except blank___________. o if the original population is not normally distributed, the sampling distribution of the mean will also be approximately normal for large sample sizes 18.Suppose you are given 3 numbers that relate to the number of people in a university student sample. The three numbers are 10, 20, and 30. If the standard deviation is 10, the standard error equals blank__________ o 5.77 19.You are tasked with finding the sample standard deviation. You are given 4 numbers. The numbers are 5, 10, 15, and 20. The sample standard deviation equals blank__________. o 6.455 20.Two methods exist to create a sampling distribution. One involves using parallel samples from a population and the other is to use the blank__________. o rules of probability 21.The hypothesis of most interest to the researcher is blank__________. o the alternative hypothesis 22.A Type I error occurs when we blank__________. o reject a true null hypothesis 23.Statisticians can translate p-values into several descriptive terms. Suppose you typically reject H0 at level 0.05. Which of the following statements is incorrect? o If the p-value 0.01, there is overwhelming evidence to infer that the alternative hypothesis is false. 24.In a criminal trial where the null hypothesis states that the defendant is innocent, a Type I error is made when blank___________. o an innocent person is found guilty 25.To take advantage of the information of a test result using the rejection region method and make a better decision on the basis of the amount of statistical evidence we can analyze the blank__________. o p-value 26.An unbiased estimator is blank_________. o a sample statistic, which has an expected value equal to the value of the population parameter 27.Thirty-six months were randomly sampled and the discount rate on new issues of 91-day Treasury Bills was collected. The sample mean is 4.76% and the standard deviation is 171.21. What is the unbiased estimate for the mean of the population? o 4.76% 28.A 98% confidence interval estimate for a population mean is determined to be 75.38 to 86.52. If the confidence level is reduced to 90%, the confidence interval for population mean blank__________. o becomes narrower 29.Suppose the population of blue whales is 8,000. Researchers are able to garnish a sample of oceanic movements from 100 blue whales from within this population. Thus, blank__________. o researchers can ignore the finite population correction factor 30.In the sample proportion, represented by p = x / n, the variable x refers to blank__________. o The number of successes in the sample 31.The distribution of the test statistic for analysis of variance is the o F-distribution 32.In Fisher's least significant difference (LSD) multiple comparison method, the LSD value will be the same for all pairs of means if o all sample sizes are the same 33.One-way ANOVA is applied to three independent samples having means 10, 13, and 18, respectively. If each observation in the third sample were increased by 30, the value of the F-statistic would o Increase 34.Assume a null hypothesis is found true. By dividing the sum of squares of all observations or SS(Total) by (n - 1), we can retrieve the blank__________. o sample variance 35.Which of the following is true about one-way analysis of variance? o n1 = n2 = … = nk is not required. 36.A tabular presentation that shows the outcome for each decision alternative under the various states of nature is called a blank__________. o payoff table 37.Which of the following statements is false regarding the expected monetary value (EMV)? o In general, the expected monetary values represent possible payoffs. 38.In the context of an investment decision, blank__________ is the difference between what the profit for an act is and the potential profit given an optimal decision. o an opportunity loss 39.The branches in a decision tree are equivalent to o events and acts 40.Which of the following is not necessary to compute posterior probabilities? o EMV 41.Which of the following statements about decision analysis is false? o Decisions can never be made without the benefit of knowledge gained from sampling 42.______ can identify when two events are relational o Conditional probability 43.An approach of assigning probabilities, which assumes that all outcomes of the experiment are equally likely is referred to as the o Classical Approach 44.The expected value of perfect information is the same as o The expected opportunity loss for the best alternative 45. Which of the following is False? o The EMV decision is always different from the EOL decision 46.A payoff table lists monetary values for each possible combination of the o Event (state of nature) and act (alternative) 47.When a person receives an email questionnaire and places it in their deleted items witout responding, they are contributing to_____ o Non-response error 48.The Notion______ represents the probability of B when A has occurred o P(B/A) 49.If A nd B are mutually exclusive events with P(A) = 0.30 and P(B) = 0.40, then P(A or B) is______ o 0.7 50.Which of the following statements is true regarding the design of a good survey? o The questions should be kept as short as possible 51.Which of he following statements is false regarding he expected monetary value (EMV) o In general, the expected monetary values represent possible payoff 52.The primary interest of designing a randomized block experiment is to____ o reduce the within- treatments variation to more easily detect differences among the treatment means 53.Which of the following is not a goal of descriptive statistics? o Estimating characteristics of the population (this is inferential) 54.Consider a probability tree for selecting to puppies without replacement. The joint probability of P(F)=2/7 and the second selection is P(F/F) = 3/10 is ___ o P(FF) = (2/7)(3/10) 55.The power of a test is measured by its capability of _______ o Rejecting a null hypothesis that is false 56.A Sample of 500 Athletes is taken from a population of 11,000 Olympic athletes to measure work ethic. As a result, we ____ o Can predict an outcome with some level of certainty 57.Assume EVPI=$50,000 and EMV=$35000. If perfect information exists the value of EPPI is _____ o 85,000 58.A summary measure that is computed from a sample to describe a characteristic of the population is called o Inferential statistics 59.In one-way analysis of variance, between-treatments variation is measured by the ___ o SST 60.A survey will be conducted to compare the United Way…3 corporations… ANOVA model will be o One-way analysis variance 61. When is the tukey multiple comparison method used o To test for difference in pairwise means 62.Which of the following statements is false o A confidence level expresses the degree of certainty that an INTERVAL will include the actual value of the SAMPLE STATISTIC 63. Though not the most efficient method rolling four dice enough times will result in theoretical probabilities being similar to____ o The relative frequency 64. The standard error is ______ o The standard deviation of the sampling distribution 65. For a given level of significance, if the sample size increases. The probability of a type II error will_____ o Decrease 66.A study is under way to determine the average height of all 32,000 adult pine trees in a certain national forest. The heights of 500 randomly selected adult pine trees are measured and analyzed. The sample in this study is o the 500 adult pine trees selected at random selected at random from this forest. 67.The average sales per customer at a home improvement store during the past year is $75 with a standard deviation of $12. The probability that the average sales per customer from a sample of 36 customers, taken at random from this population, exceeds $78 is _____ o .0668 68.Which of the following is a rule violation in hypothesis testing o We accept the null hypothesis 69. What Is Statistics? "Statistics is a way to get information from data." Statistics is a tool for creating new understanding from a set of numbers. Descriptive Statistics A student enrolled in a business undergraduate program is attending his first class of the required business statistics course. The student is somewhat apprehensive because he believes the myth that the course is difficult to pass. To alleviate his anxiety, the student asks the professor about last semester’s student grades. Since the professor is friendly and helpful, like all other statistics professors, he obliges the student and provides a list of the final grades, which are composed of semester or term work plus the final exam. What information can the student obtain from the list? This is a typical statistics problem. The student has the data (grades) and needs to apply statistical techniques to uncover the desired information. This is a function of descriptive statistics. Descriptive statistics is one of two branches of statistics which focuses on methods of organizing, summarizing, and presenting data in a convenient and informative way. One form of descriptive statistics uses graphical techniques which allow statistics practitioners to present data in ways that make it easy for the reader to extract useful information. A histogram (or bar graph) can show if the data is evenly distributed across the range of values, if it falls symmetrically from a center peak (normal distribution), if there is a peak but the more of the data falls on one side of the peak than the other (a skewed distribution), or if there are two or more peaks in the data (bi- or multi-modal). Figure 1 shows normal and skewed distributions. Next Page Descriptive Statistics Another form of descriptive statistics uses numerical techniques to summarize data. Rather than providing the raw data, the professor may only share summary data with the student. One such method that you have already used frequently calculates the average or mean. In the same way that a person can calculate the mean age of the employees of a company, the professor can compute the average grade of last semester's course. The actual technique we use depends on what specific information we would like to extract. In this example, we can see several important pieces of information. The first is the "typical" grade. We call this a measure of central location. The mean (or average) is one such measure; it is the sum of all the data values divided by the number of values. Suppose the student was told that the average grade last year was 67. Is this enough information to reduce his anxiety? The student would likely respond "no" and he would like to know whether most of the grades were close to 67 or if the grades were scattered far below and above the average. He needs a measure of variability. The simplest such measure is the range, which is calculated by subtracting the smallest number from the largest. Suppose the highest grade is 96 and the lowest grade is 24. The range of grades is 72. Unfortunately, this range calculation provides little additional information. The student also wants to know how the grades are distributed between 24 and 96. Next Page Descriptive Statistics The median is the midpoint of the distribution where 50% of the data values are higher and 50% are lower. (Note that the mean and median will not necessarily be an observed test score.) Finally, the mode is the most frequently occurring data value. The student might find it useful to know that the median score was 78 and the modal score was 80. He now knows that half the students scored 78 or higher and that 80 was the most frequently occurring test score. Apparently some very low test scores dragged the average down to 67. (See Figure 1.) There are two more measures of variability which are used in statistics. The variance is the average squared deviation from the mean. To compute the variance, the difference between each data value and the mean is calculated and squared. The mean of the resulting squared differences is the variance. Note that if the differences are not squared, their sum will always be 0. If the data values are, for example, heights in inches, the resulting variance will be measured in square inches. As we move further into our study of statistics, we will often use standard deviation as the measure of variability. Standard deviation is simply the square root of the variance and gets the variability measure back to the same units as the data. Standard deviation has many useful properties when the data is normally distributed. Next Page Figure 1: Summary Statistics 1, 3, 3, 6, 7, 8, 9 Median = 6 1, 3, 3, 4, 5 6, 8, 9 Median = 4.5 The Mode = The most occuring number. eg. Find the Mode of the list: 2 4 6 8 12 12 15 4 2 6 8 7 7 9 12 Mode = 12 eg. Find the Mode of the list: 2 8 6 4 10 12 2 4 8 8 4 Mode = 4 and 8 The mean of the data set 2, 7, 9 is 6. The median of the data set 1, 3, 3, 6, 7, 8, 9 is 6. The median of the data set 1, 2, 3, 4, 5, 6, 8, 9 is 4 plus 5 divided by 2 = 4.5. The mode of the dataset 2, 4, 6, 8, 12, 12, 15, 4, 6, 8, 7, 7, 9, 12 is 12. The modes of the dataset 2, 8, 6, 4, 10, 12, 2, 4, 8, 8, 4 are 4 and 8. A graphic with Frequency on the Y axis shows three different smooth curves. The first is a negatively skewed distribution which has a tail to the left of the peak; the mode is at the peak of the distribution with the median to the left and the mean to the left of the median. The second curve is a normal distribution which represents a perfectly symmetrical distribution where the mean, median, and mode are at the peak of the curve. The final curve is a positively skewed distribution with a tail to the right of the peak; the mode of the distribution is at the peak with the median to the right of the median and the mean to the right of the median. Next Page Descriptive Statistics Over the past several years, colleges and universities have signed exclusivity agreements with a variety of private companies. These agreements bind the university to sell that company's products exclusively on the campus. Many of the agreements involve food and beverage firms. A large university with a total enrollment of about 50,000 students has offered Pepsi-Cola an exclusivity agreement that would give Pepsi exclusive rights to sell its products at all university facilities for the next year with an option for future years. In return, the university would receive 35% of the on-campus revenues and an additional lump sum of $200,000 per year. Pepsi has been given 2 weeks to respond. The market for soft drinks is measured in terms of 12-ounce cans. Pepsi currently sells an average of 22,000 cans per week (over the 40 weeks of the year that the university operates). The cans sell for an average of 75 cents each. The costs including labor amount to 20 cents per can. Pepsi is unsure of its market share but suspects it is considerably less than 50%. Next Page Descriptive Statistics A quick analysis reveals that if its current market share were 25%, then, with an exclusivity agreement, Pepsi would sell 88,000 (22,000 is 25% of 88,000) cans per week or 3,520,000 cans per year (over the 40 weeks of university operation). The profit or loss can be calculated. The only problem is that we do not know how many soft drinks are sold weekly at the university. Pepsi assigned a recent university graduate to survey the university's students to supply the missing information. Accordingly, she organizes a survey that asks 500 students to keep track of the number of soft drinks they purchase over the next 7 days. The information we would like to acquire is an estimate of annual profits from the exclusivity agreement. The data are the numbers of cans of soft drinks consumed in 7 days by the 500 students in the sample. We can use descriptive techniques to learn more about the data. In this case, however, we are not so much interested in what the 500 students are reporting as we are in knowing the mean number of soft drinks consumed by all 50,000 students on campus. To accomplish this goal, we need the second branch of statistics called inferential statistics. Next Page Inferential Statistics Inferential statistics is a body of methods used to draw conclusions or inferences about characteristics of populations based on sample data. The population in question in this case is the soft drink consumption of the university's 50,000 students. The cost of interviewing each student would be prohibitive and extremely time consuming. Statistical techniques make such endeavors unnecessary. Instead, we can sample a much smaller number of students (the sample size is 500) and infer from the data the number of soft drinks consumed by all 50,000 students. We can then estimate annual profits for Pepsi. When an election for political office takes place, the television networks cancel regular programming and instead provide election coverage. When the ballots are counted, the results are reported. However, for important offices such as president or senator in large states, the networks actively compete to see which will be the first to predict a winner. Winner predictions are made by using exit polls, wherein a random sample of voters who exit the polling booth is asked for whom they voted. From the data the sample proportion of voters supporting the candidates is computed. A statistical technique is then applied to determine whether there is enough evidence to infer that the leading candidate will garner enough votes to win. The exit poll results from the state of Florida during the 2000 year elections were recorded (only the votes of the Republican candidate George W. Bush and the Democrat Albert Gore). The network analysts would like to know whether they can conclude that George W. Bush will win the state of Florida. Next Page Inferential Statistics Exit polls are a very common application of statistical inference. The population the television networks wanted to make inferences about is the approximately 5 million Floridians who voted for Bush or Gore for president. The sample consisted of the 765 people randomly selected by the polling company who voted for either of the two main candidates. The characteristic of the population that we would like to know is the proportion of the total electorate that voted for Bush. Specifically, we would like to know whether more than 50% of the electorate voted for Bush (counting only those who voted for either the Republican or Democratic candidate). Because we will not ask every one of the 5 million actual voters for whom they voted, we cannot predict the outcome with 100% certainty. A sample that is only a small fraction of the size of the population can lead to correct inferences only a certain percentage of the time. You will find that statistics practitioners can control that fraction and usually set it between 90% and 99%. Incidentally, on the night of the United States election in November 2000, the networks goofed badly. Using exit polls as well as the results of previous elections, all four networks concluded at 8:00 p.m. that Al Gore would win the state of Florida. Shortly after 10:00 p.m., the networks reversed course and declared that George W. Bush would win the state of Florida. By 2:00 a.m., another verdict was declared: The result was too close to call. Next Page Key Statistical Concepts Statistical inference problems involve three key concepts: the population, the sample, and the statistical inference. A population is the group of all items of interest to a statistics practitioner. It is frequently very large and may, in fact, be infinitely large. In the language of statistics, population does not necessarily refer to a group of people. It may, for example, refer to the population of diameters of ball bearings produced at a large plant. A descriptive measure of a population is called a parameter. In most applications of inferential statistics, the parameter represents the information we need. A sample is a set of data drawn from the population. A descriptive measure of a sample is called a statistic. We use statistics to make inferences about parameters. Statistical inference is the process of making an estimate, prediction, or decision about a population based on sample data. Because populations are almost always very large, investigating each member of the population would be impractical and expensive. It is far easier and cheaper to take a sample from the population of interest and draw conclusions or make estimates about the population on the basis of information provided by the sample. However, such conclusions and estimates are not always going to be correct. For this reason, we build into the statistical inference a measure of reliability. There are two such measures, the confidence level and the significance level. The confidence level is the proportion of times that an estimating procedure will be correct. When the purpose of the statistical inference is to draw a conclusion about a population, the significance level measures how frequently the conclusion will be wrong in the long run. Key Statistical Concepts Next Page Statistical Inference Statistical inference is the process of making an estimate, prediction, or decision about a population based on a sample.