BMAL 590 Quantitative Research Techniques and Statistics (SOLVED TEST)

BMAL 590 Quantitative Research Techniques and Statistics (SOLVED TEST). Decision Analysis (Section 8) 1. Which one of the following would not be considered a state of nature for a business firm? Minimum wage regulations 2. Assume an investment is made a significant number of times using the same probabilities and payoffs. In this case, the average payoff per investment represents_____. The expected payoff 3. The level of doubt regarding the decision situation where both the possible states of nature and their exact probabilities of occurrence are known as which of the following?Risk 4. The difference between expected payoff under certainty and expected value of the best act without certainty is the _________. Expected value of Perfect Information 5. Which of the following regarding EMV/EOL if false? The EMV decision is always different from the EOL decision Analysis of Variance (Section 7) 6. The F-statistic is a one-way ANOVA represents the_______. Variation between the treatments divided by the variation within the treatments 7. In _________ we can observe the effect on the response variable of at least two factors. One-way analysis of variance 8. The distribution of the test statistics for analysis of variance is the ________. F-Distribution What is Statistics? (section 1) 9. A sample of 500 athletes is taken from a population of 11,000 Olympic athletes to measure work ethic. As a result we ________. Can make consistent inferences each time work ethic is the outcome 10. When data is collected in a statistical study for only a portion or subset of all elements of interest we are using a _______. Sample Data Collecting and Sampling (section 2) 11. When a person receives an email questionnaire and places it in their deleted items without responding, they are contributing to ________. Non-response error 12. The difference between a sample mean and the population mean is called the______. Sampling error Introduction to hypothesis Testing (Section 5) 13. A type I error occurs when we _______. Reject a true null hypothesis 14. In a criminal trial where the null hypothesis states that the defendant is innocent, a Type II error is made when________. A guilty defendant is found not guilty 15. The p-value of the test is the______. The largest a at which a null hypothesis cannot be rejected Probability (Section 3) 16. Initial estimates of the probabilities of events are known as_____. Prior Probabilities 17. If the outcome of event A is not affected by event B, then events A and B are said to be ________. Independent 18. The collection of all possible outcomes of an experiment is called ________. A sample space 19. Suppose P(A) = .35. The probability of the complement of A is _______. .65 Inference about a Population (Section 6) 20. An unbiased estimator is ________. A sample Statistic, which has an expected value equal to the value of the population parameter QUIZ Section 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. 200 smartphones represents a ________. Sample Which of the following is a measure of reliability of a statistical inference? Significance level The process of using sample statistics to draw conclusions about population parameters is called_____. Doing inferential statistics Which of the following statements involve descriptive statistics as opposed to inferential statistics? The alcohol, Tobacco and Firearms Department reported that Houston had 1,790 registered gun dealers in 1997. A population of all college applicants exists who have taken the SAT exam in the US in the last year. A parameter of the population are______. SAT Scores QUIZ Section 2 -Which of the following statements is true regarding the design of a good survey? The questions should be kept as short as possible -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? Direct Observation -Manager at electronics store wants to know if customers who purchased video recorder over the last 12 months are satisfied with their products. If there are 4 different brands of video recorders made by the company, which sampling strategy would be best to use? Stratified random sample -Which of the following types of samples are almost always biased? Self-selected sampled -_____ is an expected error based only on the observations limited to a sample taken from a population. Sampling error QUIZ Section 3 Bayes’ Law is used to compute ____. Posterior Probabilities The classical approach describes a probability_________. In terms of the proportion of times that an event can be theoretically expected to occur If a set of events includes all possible outcomes of an experiment these events are considered to be________. Exhaustive Which statement is not correct?If event A does not occur, then its compliment Ai will also not occur QUIZ Section 4- The concept 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_________. The central limit theorem Each of the following are characteristics of the sampling distribution of the mean except________. If the original population is not normally distributed, the sampling distribution of the mean will also be approximately normal for large sample sizes -Suppose you are given 3 numbers that relate to the number of people in a university sample. The three numbers are 10,20,30. If the standard deviation is 10, the standard error equals___ . 5.77 You are tasked with finding the standard deviation. You are given 4 numbers. Numbers are 5, 10, 15, and 20. The standard deviation equals.6.455 Two methods exist to create a sampling distribution. Once involves using parallel samples from a population and the other is to use the______. Rules of probability QUIZ Section 5 The hypothesis of most interest to the researcher is the______. Alternative Hypothesis A Type I error occurs when________. Reject a true null hypothesis Statisticians can translate p values into several descriptive terms. Suppose you typically reject H 0 at a level of .05. Which of the following statements is incorrect? If the p value <.01, there is overwhelming evidence to infer that the alternative hypothesis is false. In a criminal trial where the null hypothesis states that the defendant is innocent a type I error is made when________. An innocent person is found guilty 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 _____. P Value Quiz Section 6 An unbiased estimator is ________. A sample Statistic, which has an expected value equal to the value of the population parameter 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? 4.76% 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 the population mean ____ Becomes Narrower 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_____ Researchers can ignore the finite population correction factor In the sample proportion, represented by p=x/n the variable x refers to: The number of succeses in the sample QUIZ Section 7 Distribution of the test statistic for the analysis of variance is the______. F-distribution In Fisher’s least significant difference (LSD) multiple comparison method, the LSD value will be the same for all pairs of means if______. All Samples are the same One-way ANOVA is applied to 3 independent samples having means 10, 13, and 18 respectively. If each observation in the 3rd sample were increased by 30, the value of the F statistic would______. Increase Assume a null hypothesis is found to be true. By dividing the sum of squares of all observations or SS (Total) by (n-1) we can retrieve the______. Sample Variance Which of the following is true about a one-way analysis of variance?N1=n2…=nk it not required QUIZ section 8 A tabular presentation that shows the outcome for each decision alternative under the various states of nature is called a ______. Payoff table Which of the following statements is false regarding the expected monetary value (EMV)? In general, the expected monetary values represent possible payoffs In the context of an investment decision, _______ is the difference between what the profit for an act is and the potential profit given an optimal decision. An opportunity Loss The branches in a decision tree are equivalent to______. Events and Acts Which of the following is not necessary to compute posterior probabilities? EMV Concerning test statistics sum of squares for error measures the ____. within treatments variation The average speed of cars passing a checkpoint is 60 miles per hour with a standard deviation of 8 miles per hoir. Fifty passing cars are clocked at random from this checkpoint. the probability that the sample mean will be between 57 and 62 miles per hour is? 0.2467 Which of the following do not represent an advantage of taking a sample: when a sampling error cannot be tolerated __________addresses unknown parameters in the real world that parallel descriptive measures of very large populations. Statistical Inference A confidence interval is defined as___________. A lower and upper confidence limit associated with all specific levels of confidence _______ are utilized to make inferences about certain population parameters. Statistics if when using the confidence interval estimator of a proportion the researcher finds there is no chance of finding success in the population, adding the number 4 to the sample size could be part of the solution, which refers to ____. The Wilson Estimate A _______ sample involves diving the population into groups then randomly selecting some of the groups and taking either a sample or a census of their members. Cluster Suppose we have a test hypothesis at a significance level of .01 where the resulting F-ratio value is 3.2. The degrees of freedom from the numerator are 10 and the denominator are 20. The p-value of the test is .0129 and we can claim the result: It is not significant at p<.01 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 ______. Sample Variance Historically, a company that mails its monthly catalog to potential customers receives orders from 8 percent of the addresses. If 500 addresses are selected randomly from the last mailing, what is the probability that between 35 and 50 orders were received from this sample? 0.7444 Section 1- What is Statistics? What is Statistics?  Statistics is a way to get information from data. It is a tool for creating new understanding from a set of numbers. 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. o 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.  Histogram (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 more of the data falls to one side (skewed distribution), or if there are two or more peaks in the data (bi-or multi-modal)  Numerical Techniques- rather than providing raw data the professor may only share summary data with the student. One such method used frequently calculates the average or mean  Measure of central location- the mean (average) is one such measure, it is the sum of all data values divided by the number of values  Range- the simplest measure of variability, is calculated by subtracting the smallest number from the largest.  Median- midpoint of the distribution where 50% of the data values are high and 50% are lower. (not that the mean and median will not necessarily be an observed test score).  Mode- the most frequently occurring data value  Variance- the average squared deviation to the mean. To compute the difference between each data value and the mean is calculated and squared. If differences are not squared sum will always be 0.  Standard deviation  - simply the square root of the variance and gets the variability measure back to the same units as the data  Negatively skewed if mean is to the left (point is to the right), positively skewed if the mean is to the right (point is to the left) Inferential Statistics  Inferential statistics is a body of methods used to draw conclusions or inferences about characteristics of population based on sample data o Example of inferential statistics is exit polling during elections o Practitioners can control the fraction of the size of the sample with between 90-99% Key Statistical Concepts  Statistical inference problems involve three concepts: o population- the group of all items of interest to a statistics practitioner. Frequently very large and may in fact be infinitely large. Does not necessarily refer to a group of people  parameter- descriptive measure of a population, represents the information we need o sample – set of data drawn from the population o statistical inference- 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.  Build in measure of reliability  Confidence level- proportion of times that an estimating procedure will be correct  Significance level- measures how frequently the conclusion will be wrong in the long run  Statistic- a descriptive measure of a sample  Populations have parameters while samples have statistics  Since Statistical inference involves using statistics to make inferences about parameters, we can make an estimate, prediction or decision about a population based on sample data  Statistical inference only deals with making conclusions about the unknown population parameters based on the observed sample statistics.  Confidence and Significance levels  Confidence level+ significance level=1 o Example- if confidence level is 95% the significance level is 5% because must equal 1 QUIZ Section 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. 200 smartphones represents a ________. Sample Which of the following is a measure of reliability of a statistical inference? Significance level The process of using sample statistics to draw conclusions about population parameters is called_____. Doing inferential statistics Which of the following statements involve descriptive statistics as opposed to inferential statistics? The alcohol, Tobacco and Firearms Department reported that Houston had 1,790 egistered gun dealers in 1997. A population of all college applicants exists who have taken the SAT exam in the US in the last year. A parameter of the population are______. SAT Scores Section 2- Data Collecting and Sampling Methods of collecting data  Statistics is a tool for converting data into information  Number of methods that produce data o Data are the observed values of a variable o We define a variable or variables that are of interest to us and then proceed to collect observations of those variables.  Three popular methods to collect data for statistical analysiso Direct Observation- ex. Number of customers entering a bank per hour  Simplest method to obtain data  Data said to be observational  Many drawback to direct observation including that it is difficult to produce useful information in a meaningful way  Advantage is low cost o Experiments- ex new ways to produce things to minimize costs  Sample is split into two groups, one who does something and the other does not then evaluate results from two groups o Surveys – one of the most familiar data collecting methods. Solicit information from people concerning such things as their income, family size and opinions on various issues. Majority are conducted for private use.  Response rate- the proportion of all people who were selected to complete the survey  Low response rate- can destroy the validity of any conclusion resulting from statistical analysis. Need to ensure data is reliable.  Personal interview- many researchers believe this is the best way to survey people, involves an interviewer soliciting information from a respondent. Has higher response rate. Main disadvantage is the cost.  Telephone interview- usually less expensive but also les personal and lower expected response rate o Self-administered questionnaire- usually mailed to sample of people. Inexpensive, but usually have low response rate, have high number of incorrect responses due to misunderstanding questions Questionnaire Design  Must be well thought out, key design principles include: o Keep short as possible o Ask short, simple, clearly worded questions, o Start with demographic questions o Use dichotomous (yes/no) and multiple choice for ran o Use open ended questions cautiously o Avoid using leading questions o Try questionnaire to small number of people first to uncover problems o Think about the way you intend to use the collected data when preparing the questionnaire Sampling  Chief motives for examining a sample rather than a population are cost and practicality  Target population – the population about which we want to draw inferences  Sampled population- actual population from which the sample has been taken  Sampled and target populations should be close to one another Simple Random Sampling  Sampling plan is a method or procedure for specifying how a sample will be taken from a population  Three different sampling plans o Simple random Sampling  Sample selected in such a way that every possible sample with the same number of observations is equally likely to be chosen  Ex. Raffle with tickets  Low cost  Can assign numbers to everyone in the population and then randomly select from numbers o Stratified random sampling  Obtained by separating the population into mutually exclusive sets or stata and then drawing simple random samples from each stratum  Ex- gender (male or female), age (number or range) occupation (professional, blue collar, clerical), household income (under $25K, over $100K, etc)  Avoid strata when there is no connection between the survey and strata, ex using religion to determine group for survey on tax increase  Advantage is ability to make inferences within each stratum to compare strata (ex looking at lowest income group favors tax increase or compare highest and lowest income groups to determine whether they differ in support of tax increase)  Stratifications must be done where the strata are mutually exclusive, meaning that each member of the population must be assigned exactly one stratum  After population has been stratified, we use simple random sampling to generate complete sample o Cluster sampling  Simple random sample of groups or clusters of elements versus a simple random sample of individual objects  Useful when it is difficult or costly to develop a complete list of the population members, also useful when population elements are dispersed geographically  Ex- randomly select block within a city to gather data from (rather than getting lists of households to use)  Cluster sampling reduces costs  Increased sampling error, as may have many similarities in those you sample Larger sample size usually means more accurate sample estimates Sampling Error  Two major types of error when sample is taken from a population: sampling error and nonsampling error  Sampling error- refers to the differences between the sample and the population that exists only because of the observation that happened to be selected for the sample. o Error that we expect to occur when we make a statement about a population that is based only on the observation contained in a sample taken from a population o Difference between the true (unknown) value of the population mean and its estimate, the sample mean, is the sampling error. Size of the deviation may be large simply due to bad luck that a particularly unrepresentative samples happened to be selected Non-Sampling Error  Non-sampling error- more serious than sampling error because taking a larger sample wont diminish the size or the possibility of occurrence of this error o Result from mistakes that are made in the acquisition of the data an from the sample observations being selected improperly o Three types of non-sampling errors: o 1-Data Acquisition errors- arise from the recording of incorrect responses. May be result of incorrect measurement taken because of faulty equipment, mistakes made during transcription from primary sources, inaccurate recording of data due to misinterpretation of terms or inaccurate responses to questions concerning sensitive issues o 2- Non-Response Error- refers to error or bias introduced when responses are not obtained from some members of the sample. When this happens sample observations may not be representative of the target population resulting in biased results.  Response rate- the proportion of all people selected who complete the survey, key survey parameter and helps in understanding the validity of the survey and sources of non-response error o 3- Selection bias- occurs when the sampling plan is such that some members of the target population cannot possibly be selected for inclusion in the sample. Together with nonresponse error selection bias  When responses are not received from a sampled person bias is introduced QUIZ Section 2 -Which of the following statements is true regarding the design of a good survey? The questions should be kept as shot as possible -Which method of data collection is involved when a researcher counts and records the umber of students wearing backpacks on campus in a given day? Direct Observation -Manager at electronics store wants to know if customers who purchased video recorder over the last 12 months are satisfied with their products. If there are 4 different brands of video recorders made by the company, which sampling strategy would be best to use? Stratified random sample -Which of the following types of samples are almost always biased? Self-selected sampled -_____ is an expected error based only on the observations limited to a sample taken from a population. Sampling error