A grudge is a heavy thing to carry.

Probability The probability of an event is the proportion of times we would expect the event to occur in an infinitely long series of identical sampling experiments.

Probability If all the possible outcomes are equally likely, the probability of the occurrence of an event is equal to the proportion of the possible outcomes characterized by the event.

Probability Probability is a very useful notion in situations involving at least some degree of uncertainty; it gives us a way of expressing the degree of assurance that a particular event will occur.

Probability Chance factors inherent in forming samples always affect sample results. Sample results must therefore be interpreted with that in mind.

Probability The probability of occurrence of either one event OR another OR… is obtained by adding their individual probabilities, provided the events are mutually exclusive.

Probability The probability of the joint occurrence of one event AND another AND another AND another… is obtained by multiplying their separate probabilities, provided the events are independent.

Probability Any relative frequency distribution may be interpreted as a probability distribution.

Probability Pr = =.85 (85% chance) GradeRelative Frequency A.15 B.30 C.40 D.10 F.05

Your CHANCECHANCECHANCECHANCE For a break coming up soon!

Confidence Statement Statistic ± Margin of Error

Margin of Error 1 n

Confidence Interval A range of values constructed from sample data so the parameter occurs within that range at a specified probability. The specified level of probability is called the level of confidence.

Confidence Interval for a Sample Mean X + Z ( ( S N

We’re CONFIDENT there’s a P R O B A B I L I T Y you want a break Stand up and take a short break

Confidence Interval 95% of those surveyed will fall into a certain range surrounding the mean 95% Confidence Interval

Confidence Interval The average size of a mortgage applied for in 1993 was $116,991 as opposed to $119,999 in A sample of 64 mortgages showed that the standard deviation of the amount applied for was $6019. Find a 95% confidence interval for the average size of a mortgage applied for in 1993.

Z = 1.96 Confidence Interval s = 6019 C =95% i n = 64 x = $116,991

Confidence Interval X ± Z( s / √n) = 116,991 ± 1.96( 6019 / √64 ) = 116,991 ± 1.96(752.38) = 116,991 ± = to

Confidence Interval According to the Family Economic Research Group of the US Department of Agriculture, middle income couples who had babies in 1992 will spend an average of $128,670 by the time the baby is 18 years old. Assume the standard deviation of a sample of 100 families was $8473. Find a 90% confidence interval for the average cost to raise a child born in 1992.

Z = n = 100 s = 8473 X = 128,670 C = 90% i Confidence Interval

X ± Z( s / √n) = 128,670 ± 1.645( 8473 / √100) = 128,670 ± 1.645(847.3) = ± = to

Confidence Interval for a Sample Proportion p + Z p ( 1 - p ( n

Confidence Interval for a Sample Proportion Suppose 1,600 of 2000 union members sampled said they plan to vote for the proposal to merge with the UMA. Using the.95 level of confidence, what is the interval estimate for the population proportion? Based on the confidence interval, what conclusion can be drawn?

p + Z p ( 1 - p ( n = (1-.80) 2,000 = =.782 and.818 Confidence Interval for a Sample Proportion

Point Estimate A value, computed from sample information that is used to estimate the population parameter

Standard Error of the Sample Mean The standard deviation of the sampling distribution of the sample means. It is a measure of the variability of the sampling distribution of the sample mean.

Look at the explanation provided in your textbook Pages Central Limit Theorem

REMINDER: Chapter 18 will be an important reference for this section of statistics

Experimental Process Subjects Treatment Observation

Variables Explanatory Variable (Independent variable) Response Variable (Dependent variable) Lurking of Confounding Variable

Alternative Experimental Designs Completely Randomized Design Block Design Matched Pairs Design Double Blind Design

Completely Randomized Design Simplest Design Strategy Each subject is randomly assigned to one group Typically, group sizes are identical

Completely Randomized DesignSubjects Group A Group B Group C AdamsX AllenX BaileyX DaltonX GrayX JamesX RobertsX SmithX WhiteX

Block Design Used when known extraneous variables may influence the experiment Subjects are pre-sorted by the influencing variables, then partitioned into similar blocks Subjects from each block are randomly assigned to groups

One-Dimensional Block Design to Control Age AgeSubjectGroup AGroup BGroup C 16Gray 17May GrayLee 20Lee 28Jones 29CooperSmithJonesCooper 29Smith 30Adams 33Brown AdamsMagee 34Magee

Matched Pairs Design Each subject receives each treatment Treatment sequence is randomly chosen for each subject

Matched Pairs Design SubjectsTreatment Order AdamsA B C AllenA C B BaileyB A C DaltonC B A GrayA B C JamesC B A RobertsB C A SmithC A B WhiteA C B

Double Blind Experiment Neither the subjects nor the investigators know which treatment is administered

Control Minimize the effects of lurking/confounding variables on the response, most simply by comparing several treatments.

Randomize Use impersonal chance to assign subjects to treatments.

Replicate Repeat the experiment on many subjects to reduce chance variation in the results.

Statistical Significance An observed effect so large that it would rarely occur by chance.