Populations, Samples, and Probability

Populations and Samples Population – Any complete set of observations (or potential observations) may be characterized as a population.

Samples Any subset of observations from a population may be characterized as a sample. Optimal sample size What 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 class Citizens of Wyoming; citizens of New York Twenty lab rats in an experiment; all lab rats, similar to those used in the experiment All U.S. presidents; all registered Republicans Two tosses of a coin; all possible tosses of a coin

Random sampling 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.

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.

Randomness How 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 numbers This 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 Assignment Random 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

Probability The 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.

Probability Mutually exclusive events – events that can’t occur together Use 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-

Probability Events 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