Stat4e TOC ISM - mastmedical.org

1 CONTENTSC hapter 1 Introduction to Statistics1 Chapter 2 Descriptive Statistics11 Chapter 3 Probability71 Chapter 4 Discrete probability Distributions97 Chapter 5 Normal probability Distributions119 Chapter 6 Confidence Intervals159 Chapter 7 Hypothesis Testing with One Sample179 Chapter 8 Hypothesis Testing with Two Samples215 Chapter 9 Correlation and Regression253 Chapter 10 Chi-Square Tests and the F-Distribution287 Chapter 11 Nonparametric Tests325 Appendix AAlternative Presentation of the Standard Normal Distribution351 Appendix CNormal probability Plots and Their Graphs352 Activities353 Case Studies357 Uses and Abuses367 Real Statistics Real AN OVERVIEW OF Try It Yourself population consists of the prices per gallon of regular gasoline at all gasoline stations inthe United sample consists of the prices per gallon of regular gasoline at the 800 surveyed data set consists of the 800 the numerical measure of $2,326,706,685 is based on the entire collection of player s salaries, it is from a the numerical measure is a characteristic of a population, it is a statistics involve the statement 76% of women and 60% of men had a physicalexamination within the previous year.

2 Inference drawn from the study is that a higher percentage of women had a physicalexamination within the previous EXERCISE sample is a subset of a is usually impractical (too expensive and time consuming) to obtain all the population parameter is a numerical description of a population characteristic. A statistic is anumericaldescription of a sample statistics and inferential A statistic is a numerical measure that describes a sample Inferential statistics involves using a sample to draw conclusions about a A population is the collection of alloutcomes, responses, measurements, or countsthat are of data set is a population because it is a collection of the ages of all the members of theHouse of data set is a sample because only every fourth person is data set is a sample because the collection of the 500 spectators is a subset within thepopulation of the stadium s 42,000 data set is a population because it is a collection of the annual salaries of all lawyers at a 2009 Pearson Education, Inc.

3 , Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently portion of this material may be reproduced, in any form or by any means, without permission in writing from the to , because the collection of the 20 patients is a subset within the data set is a population since it is a collection of the number of televisions in all : Party of registered voters in Warren : Party of Warren County voters responding to phone : Major of college students at Caldwell : Major of college students at Caldwell College who take : Ages of adults in the United States who own : Ages of adults in the United States who own Dell : Income of all homeowners in : Income of homeowners in Texas with : All adults in the United States that take : Collection of 1000 adults surveyed that take : Collection of all infants in : Collection of the 33,043 infants in the : Collection of all households in the : Collection of 1906 households.

4 Collection of all computer : Collection of 1000 computer users : Collection of all registered : Collection of 1045 registered voters : Collection of all students at a : Collection of 496 college students : Collection of all women in the : Collection of the 546 women : Collection of all : Collection of the 791 vacationers The value $68,000 is a numerical description of a sample of annual 43% is a numerical description of a sample of high school The 62 surviving passengers out of 97 total passengers is a numerical descriptionof all of the passengers of the Hindenburg that 44% is a numerical description of the total number of 8% is a numerical description of a sample of computer 12% is a numerical description of all new 1|INTRODUCTION TO STATISTICS 2009 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently portion of this material may be reproduced, in any form or by any means, without permission in writing from the 53% is a numerical description of a sample of people in the United is a numerical description of ACT scores for all statement 56% are the primary investor in their household is an application ofdescriptive inference drawn from the sample is that an association exists between women andbeing the primary investor in their statement spending at least $2000 for their next vacation is an application ofdescriptive inference drawn from the sample is thatU.

5 Are associated with spending more than $2000 for their next will (a) The volunteers in the study represent the sample.(b) The population is the collection of all individuals who completed the math test.(c) The statement three times more likely to answer correctly is an application of descriptive statistics.(d) An inference drawn from the sample is that individuals who are not sleep deprived willbe three times more likely to answer math questions correctly than individuals who aresleep (a) An inference drawn from the sample is that senior citizens who live in Florida have better memory than senior citizens who do not live in Florida.(b) It implies that if you live in Florida, you will have better (a) An inference drawn from the sample is that the obesity rate among boys ages 2 to 19 is increasing.(b) It implies the same trend will continue in future will DATA Try It Yourself data set contains names of cities and the other contains city : NonnumericalPopulation: : QualitativePopulation: QuantitativeCHAPTER 1 |INTRODUCTION TO STATISTICS3 2009 Pearson Education, Inc.

6 , Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently portion of this material may be reproduced, in any form or by any means, without permission in writing from the (1) The final standings represent a ranking of basketball teams.(2) The collection of phone numbers represents labels. No mathematical computations canbe (1) Ordinal, because the data can be put in order.(2) Nominal, because you cannot make calculations on the (1) The data set is the collection of body temperatures.(2) The data set is the collection of heart (1) Interval, because the data can be ordered and meaningful differences can be calculated, but it does not make sense writing a ratio using the temperatures.(2) Ratio, because the data can be ordered, can be written as a ratio, you can calculatemeaningful differences, and the data set contains an inherent EXERCISE and , Interval, and Data at the ordinal level can be qualitative or For data at the interval level, you can calculate meaningful differences between dataentries.

7 You cannot calculate meaningful differences at the nominal or ordinal More types of calculations can be performed with data at the interval level than withdata at the nominal Data at the ratio level can be placed in a meaningful , because telephone numbers are merely , because the daily high temperature is a numerical , because the lengths of songs on an MP3 player are numerical , because the player numbers are merely , because the poll results are merely , because the diastolic blood pressure is a numerical Ordinal. Data can be arranged in order, but differences between data entriesmake no No mathematical computations can be made and data are categorizedusing No mathematical computations can be made and data are categorizedusing Ratio. A ratio of two data values can be formed so one data value can beexpressed as a multiple of Ordinal. The data can be arranged in order, but differences between dataentries are not Ratio. The ratio of two data values can be formed so one data value can beexpressed as a multiple of 1|INTRODUCTION TO STATISTICS 2009 Pearson Education, Inc.

8 , Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently portion of this material may be reproduced, in any form or by any means, without permission in writing from the (a) Interval(b) Nominal(c) Ratio(d) Ordinal24.(a) Interval(b) Nominal(c) Interval(d) inherent zero is a zero that implies none. Answers will will EXPERIMENTAL Try It Yourself Solutions1a.(1) Focus: Effect of exercise on relieving depression.(2) Focus: Success of (1) Population: Collection of all people with depression.(2) Population: Collection of all university (1) Experiment(2) is no way to tell why people quit smoking. They could have quit smoking either fromthe gum or from watching the experiments could be done; one using the gum and the other using the : start with the first digits 92630782 .. , 7, 40, 19, 264a.(1) The sample was selected by only using available students.(2) The sample was selected by numbering each student in the school, randomly choosing astarting number, and selecting students at regular intervals from the starting (1) Because the students were readily available in your class, this is convenience sampling.

9 (2) Because the students were ordered in a manner such that every 25th student is selected,this is systematic EXERCISE an experiment, a treatment is applied to part of a population and responses are an observational study, a researcher measures characteristics of interest of part of a population but does not change existing census includes the entire population; a sample includes only a portion of the numbers to each member of the population and use a random number table or use arandom number 63 07 82 40 19 26 CHAPTER 1 |INTRODUCTION TO STATISTICS5 2009 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently portion of this material may be reproduced, in any form or by any means, without permission in writing from the is the repetition of an experiment using a large group of subjects. It is importantbecause it gives validity to the A double-blind experiment is used to decrease the placebo Using stratified sampling guarantees that members of each group within a populationwill be A census is a count of an entire To select a systematic sample, a population is ordered in some way and then membersof the population are selected at regular this study, you want to measure the effect of a treatment (using a fat substitute) on thehuman digestive system.

10 So, you would want to perform an would be nearly impossible to ask every consumer whether he or she would still buy aproduct with a warning label. So, you should use a survey to collect these it is impractical to create this situation, you would want to use a the Congress keeps accurate financial records of all members, you could take (a) The experimental units are the 30 35 year old females being given the treatment.(b) One treatment is used.(c) A problem with the design is that there may be some bias on the part of the researchersif he or she knows which patients were given the real drug. A way to eliminate thisproblem would be to make the study into a double-blind experiment.(d) The study would be a double-blind study if the researcher did not know which patientsreceived the real drug or the (a) The experimental units are the people with early signs of arthritis.(b) One treatment is used.(c) A problem with the design is that the sample size is small.