Slide 1Practice ProblemsAdditional Reading and ExamplesSlide 4InferenceInferenceMotivating ExampleMotivating ExampleMotivating ExampleMotivating ExampleMotivating ExampleMotivating ExampleMotivating ExampleMotivating ExampleMotivating ExampleConfidence IntervalsConfidence IntervalsConfidence IntervalsMotivating ExampleConfidence IntervalsConfidence IntervalsConfidence IntervalsMotivating ExampleConfidence IntervalConfidence IntervalConfidence IntervalConfidence IntervalConfidence LevelConfidence IntervalConfidence Interval - InterpretationMotivating ExampleExample 56Example 56Example 56Example 56Example 56Example 56Example 56Confidence IntervalConfidence IntervalInferenceTests of SignificanceMotivating ExampleTests of SignificanceTests of SignificanceTests of SignicanceMotivating ExampleGeneral Terms and CharacteristicsMotivating ExampleTests of SignificanceTests of SignificanceTests of SignificanceTests of SignificanceSlide 54STAT 210Lecture 24Introduction to Confidence IntervalsOctober 23, 2017Practice ProblemsPages 187 and 188Relevant problems: VII.1, VII.2, VII.3, and VII.4Recommended problems: VII.1, VII.2, VII.3, VII.4Additional Reading and ExamplesRead pages 185 and 186Top Hat 2InferenceStatistical inference involves using statistics computed from data collected in a sample to make statements (inferences) about unknown population parameters.Two types of statistical inference are estimation of parameters using confidence intervals and statistical tests about parameters.In this chapter we learn the basic concepts associated with confidence intervals and with statistical tests.InferenceThe first step in any inference procedure is to state the practical question that needs to be answered. This involves specifying the population of interest, and then the specific parameter that inferences need to be made about.Motivating ExampleSuppose the population is all students at this university.There are two parameters:p = the proportion of all students at this university who have childrenm = mean IQ of all students at this universityMotivating ExampleSuppose the population is all students at this university.There are two parameters:p = the proportion of all students at this university who have childrenm = mean IQ of all students at this universityDoes anyone know the proportion of all students at this university who have children?Motivating ExampleSuppose the population is all students at this university.There are two parameters:p = the proportion of all students at this university who have childrenm = mean IQ of all students at this universityDoes anyone know the mean IQ of all students at this university?Motivating ExampleSuppose the population is all students at this university.There are two parameters:p = the proportion of all students at this university who have childrenm = mean IQ of all students at this universitySince data for all students is not known, it is likely not possible to determine the value of either parameter. This is when statistical inference comes into action.Motivating ExampleSuppose the population is all students at this university.If the parameter is p = the proportion of all students at this university who have children, and if data for all students is not available, what could we do?Motivating ExampleSuppose the population is all students at this university.If the parameter is p = the proportion of all students at this university who have children, and if data for all students is not available, what could we do?1. Select a sample from the population.2. Collect data for students in the sample.3. Compute the proportion of the students in the sample that have children. Being from the sample, this is a statistic. Top HatMotivating ExampleSuppose the population is all students at this university.The parameter is p = the proportion of all students at this university who have children, and is unknown.From our sample of _______ students, _____ have children. So the proportion of the sample who have children is _________.This is an estimate of the parameter.Motivating ExampleSuppose the population is all students at this university.The parameter is p = the proportion of all students at this university who have children, and is unknown.From our sample of _______ students, _____ have children. So the proportion of the sample who have children is _________.Do you think the proportion of all students with children is exactly ______?Motivating ExampleSuppose the population is all students at this university. The parameter is p = the proportion of all students at this university who have children, and is unknown.From our sample of _______ students, _____ have children. So the proportion of the sample who have children is _________. Do you think the proportion of all students with children is exactly ______?Most likely no, and the statistical inference procedure that handles this situation is called a confidence interval.Confidence IntervalsConfidence intervals are statistical procedures that allow for the estimation of unknown population parameters.The procedure involves both the calculation of the interval, and then the interpretation of the interval. The interpretation is the statistical inference.Confidence IntervalsTo estimate an unknown population parameter we begin by selecting a sample from the population. Once the sample is selected, we then collect the necessary information from those in the sample.The data collected from the sample is used to compute a statistic, and this statistic becomes the starting point for the confidence interval and hence the statistical inference.Confidence IntervalsThe data collected from the sample is used to compute a statistic, and this statistic becomes the starting point for the confidence interval and hence the statistical inference.The value computed from the sample data collected is referred to as the point estimate of the unknown population parameter.Motivating ExampleSuppose the population is all students at this university. The parameter is p = the proportion of all students at this university who have children, and is unknown.From our sample of _______ students, _____ have children. So the proportion of the sample who have children is _________.This sample proportion p = ____ is the point estimate of p = the proportion of all students at the university with children.Confidence IntervalsIf the sample is representative of the population, then one would expect that the point estimate will be a good estimate of the
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