Probability and Statistics Chapter 1 Notes

Transcription

1 Probability and Statistics Chapter 1 Notes I Section 1-1 A is the science of collecting, organizing, analyzing, and interpreting data in order to make decisions 1 is information coming from observations, counts, measurements, or responses a There are 2 types of data sets 1) the collection of all outcomes, responses, measurements, or counts that are of interest a) the set of possible measurements, counts or observations that are of interest in a particular study 2) A subset of the population a) Since it is usually or even in terms of time or money to obtain every response, we must often rely on obtained from a b) : -- A sample in which every member of the population has an equal chance of belonging b There are 2 types of numerical descriptions 1) A numerical description of a population characteristic 2) A numerical description of a sample characteristic B Branches of Statistics 1 a The branch of statistics that involves the,, and of data 2 a The branch of statistics that involves using a to draw conclusions about a 1) A basic tool in the study of inferential statistics is II Section 1-2 A Types of Data 1 a Attributes, labels or entries 2 a measurements or counts B of

2 1 a Consists of,,, or 1) Example: type of car you drive b Can put data into, but we are unable to determine if one piece of data is or than another c When numbers are used as labels, such as on an athletic jersey, they are classified as 2 a Designations or numerical rankings which can be arranged in or order 1) TV ratings for #1 show, #2 show, etc b We can compare rankings as to which is higher, however it does not make sense to subtract one rank value from another 1) Differences in rankings are not meaningful computations 3 a Can be subtracted to find the difference between two values, put in order, and put into b Data is ; 0 can be used to indicate a position in time or space, however, the zero at this level does not correspond to none of the specific variable being measured 1) The position on the thermometer of zero degrees does not indicate that is absolutely no +heat present c Differences between data values are but it does not make sense to compare one data value as being twice (or any multiple of) another 1) The two most common uses are for, and 4 a The level of measurement 1) The number of gallons of gasoline you put into your car today b There is a on this scale which is interpreted as of the variable in question 1) It is possible to put zero gallons of gas into your tank today 2) This is called an c It is meaningful to say one measure is two times, or three times, as much as another 1) You may have put twice as much gas in your car today than you did last week 5 How to tell Interval data from Ratio data a Does the expression have any meaning in the context of the data?

3 1) $2 is twice as much as $1, so these data points are at the 2) A temperature of 2 degrees is twice as warm as 1 degree is, so these data points are at the b Interval data is relating to either or 1) Remember, time and time are the same thing III Section Experimental Design A Design of a Statistical Study 1 Identify the (the focus) and the of the study 2 Develop a for 3 the data 4 the data, using techniques 5 the data and about the using statistics 6 any possible B Data Collection 1 Do an Observational Study a and characteristics of interest of of a population, but do NOT change 2 Do an Experiment a Apply a to part of a and responses or results b Observe another part of the population as a 1) May use a in place of the treatment being tested 3 Use a simulation a Use a or model to the conditions of a situation or process 1 allow us to study that are or even to create in real life a) Testing the effects of alcohol on a pilot s ability to fly is best done in a flight simulator b) Predicting how quickly and how far a disease may spread is also best done using a computer model 2 Simulations often save 4 Use a survey (census) a A survey is an of one or more of a

4 1) Usually carried out on by asking them to respond to questions b It s important to word the questions so that they do not lead to C Experimental Design 1 Experiments must be carefully designed in order to produce meaningful, unbiased, results a The occurs in an experiment when subjects change their behavior simply because they know they are participating in an experiment 2 Three key elements of a well-designed experiment are,, and a Control 1) It is important to as many as possible in a study 2) When an experimenter cannot tell the difference between the effects of different factors in an experiment, a has occurred 3) occurs when a subject reacts favorably to a placebo when in fact they have been given no medical treatment at all a) is a technique used in which the subject does not know whether he or she a receiving a real treatment or a placebo b) experiments occur when neither the subjects nor the experimenter knows whether an individual subject is receiving a treatment or a placebo 1 The experimenter only finds out which subjects are which all the data have been collected b Randomization is a of assigning to treatment groups 1) Divide subjects with into blocks, and then split each block up into treatment groups 2) - Subjects are paired up according to a a) One subject in each pair is selected to receive one treatment, while the other one gets another, treatment c Replication is the of an using a of 1) The the sample size, the

5 D Sampling Techniques 1 (or survey) a or of an a Provides complete information, but is often too costly or difficult to perform 2 a or of of a a Researcher must ensure that the sample is of the 1) This is necessary to that about a are a) the between the of a and of the b a sample in which of the has an chance of being 1) Methods of sampling randomly a) assign each member of the population a number and then randomly select the numbers that you will survey 1) Random number table (Appendix B of the book) a pick a starting point b Count off digits in groups that match how many your has c Record the numbers, those that are larger than the population size 2) Calculator a Math, PRB, 5(randInt) b Enter the that you started with when assigning labels to your population, then a comma, then the number you assigned, comma, and the sample you wish to use 1 The calculator will generate the requested quantity of random numbers 3) If you do not want to have any member of the population included in the sample twice, the sampling process is said to be 4) If you don t care if a member of the population is included twice, the sampling process is said to be b) 1) Separate into two or more, called, using some

6 c) d) e) a select members of each to make up your 1) When the is into that are to each other, you could randomly select a of (not all the groups) and do your data collection on those groups a We call these groups 1) Each of the is assigned a a Put the of the population in somehow b Randomly select a point c Randomly select an d Survey every member of the from your 1)!! a Simply select those members of the population who are