Chapter 8Populations, Samples, and Probability

Populations and SamplesPopulation –

Any complete set of observations (or potential observations) may be characterized as a population.

SamplesAny subset of observations from a population

may be characterized as a sample.

Optimal sample sizeWhat is the estimated variability among

observations?What is an acceptable amount of error in our

conclusion?

Progress Check 8.1 (p 176)For each of the following pairs, indicate

whether the relationship between the first and second expressions could describe a sample and its population.Students in the last row; students in classCitizens of Wyoming; citizens of New YorkTwenty lab rats in an experiment; all lab rats,

similar to those used in the experimentAll U.S. presidents; all registered RepublicansTwo tosses of a coin; all possible tosses of a

coin

Random samplingSampling is random if,

at each stage of sampling,

the selection process guarantees that all remaining observations in the population have equal chances of being included in the sample.

Progress Check 8.3 (p 177)True or False given a random selection of ten

playing cards from a deck of 52 cards implies that

The random sample of ten cards accurately represents the important features of the whole deck

Each card in the deck has an equal chance of being selected

It is impossible to get ten cards from the same suit

Any outcome, however unlikely, is possible.

RandomnessHow can you ensure that a sample is

randomly chosen?

Sampling is random if, at each stage of sampling, the selection process guarantees that all remaining observations in the population have equal chances of being included in the sample.

Table of random numbersThis table can be use to obtain a random

sample.

Use the random number table (H page 530) to select a random sample of 5 students from this class.

Random AssignmentRandom assignment refers to a procedure

designed to ensure that each subject has an equal chance of being assigned to an group in an experiment.

This accounts for the possibility that the sampling procedure may have been from a hypothetical population which was not available at the time of sampling.

Example of random number generation

ProbabilityThe proportion or fraction of times that a

particular event is likely to occur.

Common outcomes signify, most generally, alack of evidence that something special has occurred.

Rare outcomes signify that something special has occurred, and any comparable study would most likely produce a mean difference with the same sign and a similar value.

ProbabilityMutually exclusive events – events that

can’t occur togetherUse the addition rule (AND)

The probability that two independent events occurring together is equal to the probability of one occurring plus the probability of the second occurring

Probability of blood type

What is the probability that 2 people out of 100 will have A+ and A- blood types.

Out of 100 donors

84 donors are RH+ 16 donors are RH-

38 are O+ 7 are O-

34 are A+ 6 are A-

9 are B+ 2 are B-

3 are AB+ 1 is AB-

ProbabilityEvents not mutually exclusive use the

multiplication rule. (OR)The probability of one event has no effect on

the occurrence of a second event.The probability that two events will occur at

the same time is equal to the product of their probabilities.

Probability of winning the lottery

How do they calculate that number?Webmath page

Video – birthday probability problem