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Error of the estimate: Are the predicted values good estimates of the actual dependent values? Histogram and a Frequency Polygon for Problem 2. Computations of statistics from grouped data are based on class midpoints rather than raw values. At least one of the 3 populations is different 3-day Quality Mgmt.
The empirical rule will be referred to quite often throughout the course. It can be emphasized in this chapter that there are at least two major dimensions along which data can be described. Students can understand that a measure of central tendency is often not enough to fully describe data. A second major group of descriptive statistical techniques are the measures of variability. P a g e 68 example. In addition. The Pearsonian coefficient of skewness is a handy tool for ascertaining the degree of skewness in the distribution.
The coefficient of correlation is introduced here instead of chapter 14 regression chapter so that the student can begin to think about two-variable relationships and analyses and view a correlation coefficient as a descriptive statistic. Box and Whisker plots can be used to determine the presence of skewness in a distribution and to locate outliers. It should be emphasized that the calculation of measures of central tendency and variability for grouped data is different than for ungrouped or raw data.
All in all. While the principles are the same for the two types of data. Computations of statistics from grouped data are based on class midpoints rather than raw values. Measures of shape are useful in helping the researcher describe a distribution of data.
That is. Since there are an even number of terms. Since there are an odd number of terms. P a g e 72 4 is the most frequently occurring value 3. Rearranging the data into ascending order: Q3 is located at the Q1 is located at the 6. Arranging the data in order: P a g e 98 between 14 and 62? Since the normal distribution is symmetrical.
Exceed 41 days: Exceed 37 days: P a g e Since the distribution is normal. P a g e Bordeaux: The modal class is 0 — 2. The modal class is 2. Standard Deviation: This computed group mean. While many of the stock prices are at the cheaper end. The difference again is due to the grouping of the data and the use of class midpoints to represent the data.
The class midpoints due not accurately reflect the raw data. More people are older but the most extreme ages are younger ages. There are no mild or extreme outliers. The only mild outlier is The distribution is positively skewed since the median is nearer to Q1 than Q3.
P a g e Outer Fences: Median is the average of the 15th and 16th value. P a g e Exxon Mobil: Mineral Production 1 2 3 Mineral Production 4 5. P a g e Inner Fences: The 4. The Modal Class is Each of the numbers. Each of the points.
Albania x x2 4. This worker is in the lower workers but within one standard deviation of the mean.
The distribution is skewed to the right because the mean is greater than the median. There are no outliers in the lower end. There are three dominating. Since the median is nearer to Q1.
There are two extreme outliers in the upper end South Louisiana. There is one mild outlier at the upper end New York. Since 1. P a g e Boxplot of U. Ports 3. Ports 50 U. Select the appropriate law of probability to use in solving problems.
Comprehend the different ways of assigning probability. Understand and apply marginal. Students enjoy rolling dice.
An attempt has been made to differentiate the several types of probabilities so that students can sort out the various types of problems. Solve problems using the laws of probability. Probability problems are so varied and individualized that a significant portion of the learning comes in the doing. Revise probabilities using Bayes' rule. If the student is aware that what they have at their hands is an array of tools or techniques.
Of all the chapters in the book. The text attempts to emphasize this point and underscore it by presenting several different ways to solve probability problems. This particular chapter is very amenable to the use of visual aids. In teaching students how to construct a probability matrix. This chapter is frustrating for the learner because probability problems can be approached by using several different techniques. Experience is an important factor in working probability problems.
The probability rules and laws presented in the chapter can virtually always be used in solving probability problems. P a g e Section 4. Sampling from a Population Without Replacement. A4 A6 D1 A6. A4 A5 D1 A5. A5 A6 There are 15 members of the sample space The probability of selecting exactly one defect out of two is: D2 A4.
D3 A4. D2 A5. D2 A6. D3 A5 D1 D3. D2 D3. D3 A6 D1 A4. D1 D2. D1 A3 A4. D1 A2 A4. D1 A2 A3. D1 A1 A3. D1 D2 A4.
D1 A1 A4. A1 A2 A3. D2 A1 A2. A1 A3 A4. D2 A3 A4. D2 A1 A3. D2 A2 A4. D2 A1 A4. D2 A2 A3. A1 A2 A4. D1 D2 A2. D1 A1 A2.
A2 A3 A4 Combinations are used to counting the sample space because sampling is done without replacement. D1 D2 A3. B mutually exclusive. P a g e We need to know the probability of the intersection of A and T. Possession of cable TV and 2 or more TV sets are not mutually exclusive. The answer to b is found in the Yes for U and no for I cell.
It can be determined by taking the marginal. To compute this cell. Take the marginal. C Yes S No Yes. A Yes S No Yes.. O Yes No Yes. Q Yes E No Yes. S Yes Yes No. S R Yes No Yes. Variables 1 and 2 are not independent. K Yes T No Yes. L Yes No Yes. Reduce Yes Save No Yes. From P R. To solve for P P. In constructing the matrix. The respondent could not select more than one answer. Distinguish between discrete random variables and continuous random variables.
Decide when binomial distribution problems can be approximated by the Poisson distribution and know how to work such problems.
Know how to determine the mean and variance of a discrete distribution. Identify the type of statistical experiments that can be described by the binomial distribution and know how to work such problems. Decide when to use the Poisson distribution in analyzing statistical experiments and know how to work such problems. Graphing binomial and Poisson distributions affords the student the opportunity to visualize the meaning and impact of a particular set of parameters for a distribution.
The parameters involved in the binomial distribution n and p are different from the parameter Lambda of a Poisson distribution. It is sometimes difficult for students to know how to handle Poisson problems in which the interval for the problem is different than the stated interval for Lambda. It is often difficult for students to determine which type of distribution to apply to a problem. Solving for the mean and standard deviation of binomial distributions prepares the students for chapter 6 where the normal distribution is sometimes used to approximate binomial distribution problems.
Note that in such problems. P a g e Chapters 5 and 6 introduce the student to several statistical distributions. The Poisson distribution applies to rare occurrences over some interval. The binomial tables presented in this text are non cumulative. It is important to differentiate applications of the Poisson distribution from binomial distribution problems. Lambda is a long-run average that can be appropriately adjusted for various intervals.
This makes it easier for the student to recognize that the table is but a listing of a series of binomial formula computations. In a sense. The approach taken in presenting the binomial distribution is to build on techniques presented in chapter 4. It is important to differentiate between the discrete distributions of chapter 5 and the continuous distributions of chapter 6. From there. It can be helpful to take the time to apply the law of multiplication for independent events to a problem and demonstrate to students that sequence is important.
P a g e distribution approaches the normal curve as p gets nearer to. In this text as in most because of the number of variables used in its computation. Using Table A. Lambda must be changed to the same interval twice the size: From Table A. Perhaps the value of. The interval length has been increased by 1. Ship channel and weather conditions are about normal for this period. There is no compelling reason to reject the lambda value of 0. Safety awareness is about normal for this period.
P a g e The result is likely to happen almost half the time An investigation of particular characteristics of this region might be warranted. Were officers selected based on leadership. A researcher might want to further investigate this result to determine causes.
P a g e from Table A. Other reasons for such a low number of walk-ins might be that she is retaining more old customers than before or perhaps a new competitor is attracting walk-ins away from her. New Lambda: If this actually happened. Appreciate the importance of the normal distribution. Decide when to use the normal distribution to approximate binomial distribution problems and know how to work such problems.
Recognize normal distribution problems and know how to solve such problems.
Decide when to use the exponential distribution to solve problems in business and know how to work such problems. Understand concepts of the uniform distribution. P a g e Chapter 5 introduced the students to discrete distributions. It is very helpful for the student to get into the habit of constructing a normal curve diagram. Many students tend to be more visual learners than auditory and these diagrams will be of great assistance in problem demonstration and in problem solution.
The correction for continuity is emphasized. Since this is often a stumbling block for students to comprehend. This chapter contains a section dealing with the solution of binomial distribution problems by the normal curve. The exponential distribution can be taught as a continuous distribution.
In this text. This chapter introduces the students to three continuous distributions: This also will allow the student to observe how good the approximation of the normal curve is to binomial problems. The normal distribution is probably the most widely known and used distribution. It should be emphasized.
The student can see that while the Poisson distribution is discrete because it describes the probabilities of whole number possibilities per some interval. The text has been prepared with the notion that the student should be able to work many varied types of normal curve problems.
Examples and practice problems are given wherein the student is asked to solve for virtually any of the four variables in the z equation. The z value is negative since x is below the mean. Table A. Using the z value of If The z value associated with. Since From table A. The z score associated with this area is Do not use the normal distribution to approximate this problem.
The problem can be approximated by the normal curve. Approximation by the normal curve is sufficient. The normal curve is not a good approximation to this problem. It is okay to use the normal distribution to approximate this problem Correcting for continuity: It is okay to use the normal distribution as an approximation on parts a and b.
The normal curve approximation is sufficient. P a g e correcting for continuity: P a g e From Table A. P a g e from table A. It is okay to use the normal distribution to approximate this problem.
It is okay to use the normal distribution to approximate this binomial problem. Change Lambda to: Since Lambda and x are for different intervals. About One hundred percent of the time there are less than or equal to 34 sales associates working and never more than The probability that a rod weighs less than or equal to mg is. P a g e less than or equal to mg is 1. The probability that there is less than. The probability that there is.
It is almost certain that there will be less than 2. Be aware of the different types of errors that can occur in a study. The probability that there is more than 1 or 10 minutes between arrivals is. Understand the impact of the central limit theorem on statistical analysis. P a g e minutes or more between arrivals is. Distinguish between random and nonrandom sampling.
Decide when and how to use various sampling techniques. Determine when to use sampling instead of a census. Reasons for sampling versus taking a census are given. The first portion of chapter 7 deals with sampling. It is important. Most of these reasons are tied to the fact that taking a census costs more than sampling if the same measurements are being gathered. Use the sampling distributions of and. Histograms of the means for random samples of varying sizes are presented. The central limit theorem opens up opportunities to analyze data with a host of techniques using the normal curve.
Students are then exposed to the idea of random versus nonrandom sampling. This will help to assure that they will not make poor decisions based on inaccurate and poorly gathered data. Note also by observing the values on the bottom axis that the dispersion of means gets smaller and smaller as sample size increases thus underscoring the formula for the.
Section 7. Random sampling appeals to their concepts of fairness and equal opportunity. Chapter 7 presents formulas derived from the central limit theorem for both sample means and sample proportions. Taking the time to introduce these techniques in this chapter can expedite the presentation of material in chapters 8 and 9.
As the student sees the central limit theorem unfold. P a g e Sampling Error Nonsampling Errors x 7. A union membership list for the company. White pages of the telephone directory for Utica. List of boat manufacturer's employees. Airline company list of phone and mail purchasers of tickets from the airline during the past six months. Cable company telephone directory. Utility company list of all customers. Membership list of cable management association. List of members of a boat owners association.
New York. A list of all employees of the company. A list of frequent flyer club members for the airline. P a g e f Manufacturing.
The human resource department probably has a list of company employees which can be used for the frame. Counties Go to the district attorney's office and observe the apparent activity of various attorney's at work.
States beside which the oil wells lie ii. Select some men and some women. States ii. Select some who are very busy and some who seem to be less active. Select attorneys with different ethnic backgrounds.
Counties ii. Companies that own the wells i. Select some who appear to be older and some who are younger. Approach those executives who appear to be friendly and approachable. Metropolitan areas i. Screen out personal computer owners. Go to a computer show at the city's conference center and start interviewing people. Suppose you get enough people who own personal computers but not enough interviews with those who do not.
Go to a mall and start interviewing people. P a g e from Table A.. You cannot use numbers from to Randomly sample from the random number table until 60 different usable numbers are obtained.
Take a random sample of employees from each selected factory. Divide the United States into regions of areas. Take a random sample from each of the selected area distribution centers and retail outlets. Do the same for distribution centers and retail outlets. Select a few areas. P a g e Use a table of random numbers to select a value between 0 and 40 as a starting point. With a census. There is more time for trust to be built between employee and interviewer resulting in the potential for more honest.
More time can be spent with each employee. Probing questions can be asked. Decision-makers are sometimes more comfortable with a census because everyone is included and there is no. A census appears to be a better political device because the CEO can claim that everyone in the company has had input. P a g e sampling error.. P a g e Japan: Economic Class. Education d Age.
Geographic Region. Party Affiliation. Gender b Age. Economic Class c Age. Estimate the population variance from a sample variance. Estimate the minimum sample size necessary to achieve given statistical goals. Know the difference between point and interval estimation.
P a g e Chapter 8 Statistical Inference: Estimate a population proportion from a sample proportion. From this. Examples might be proportion of people carrying a VISA card. In most cases. It should be pointed out. The confidence interval formulas for large sample means and proportions can be presented as mere algebraic manipulations of formulas developed in chapter 7 from the Central Limit Theorem. In an effort to understand the impact of variables on confidence intervals.
Proportions are computed by counting the number of items containing a characteristic of interest out of the total number of items. It is very important that students begin to understand the difference between mean and proportions. Such consideration helps the student see in a different light the items that make up a confidence interval. Business students probably understand that increasing sample size costs more and thus there are trade-offs in the research set-up.
In this chapter. Means can be generated by averaging some sort of measurable item such as age. The student can see that increasing the sample size reduces the width of the confidence interval.
The use of the chi-square statistic to estimate the population variance is extremely sensitive to violations of this assumption. A formula is given in chapter 8 for estimating the population variance. Emphasize that this applies only when the population is normally distributed because it is an assumption underlying the t test that the population is normally distributed. For this reason. The student will observe that the t formula is essentially the same as the z formula and that it is the table that is different.
One of the more common questions asked of statisticians is: Because of this. An assumption underlying the use of this technique is that the population is normally distributed. The t Distribution Robustness Characteristics of the t Distribution. Error of the estimate: The confidence interval is: The sample size is 26 skiffs. One might conclude that. P a g e The interval is inconclusive. Since zero is in the interval. Eighty-four bulbs were included in this study. Chapter 9 Statistical Inference: Know how to implement the HTAB system to test hypotheses.
Test hypotheses about a single population proportion. Test hypotheses about a single population variance. Of these. Understand the logic of hypothesis testing and know how to establish null and alternate hypotheses. Hypothesis testing presents the logic in which ideas. Find a copy in the library Finding libraries that hold this item Details Material Type: Internet resource Document Type: Ken Black Find more information about: Ken Black.
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