Lecture_20,_Chap_10,_Sec_2a

# Lecture_20,_Chap_10,_Sec_2a - Chapter 10 Section 2 Testing...

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Chapter 10 Section 2 Testing Claims about a Population Mean Assuming the Population Standard Deviation is Known

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Hypothesis Test for Mean – σ Known Learning objectives Understand the logic of hypothesis testing Test a claim about a population mean with σ known using the classical approach Test a claim about a population mean with σ known using P -values Test a claim about a population mean with σ known using confidence intervals Understand the difference between statistical significance and practical significance 1 2 3 5 4
Logic of Hypothesis Testing We have the outline of a hypothesis test, just not the detailed implementation How do we quantify “unlikely”? How do we calculate Type I and Type II errors? What is the exact procedure to get to a do-not- reject / reject conclusion?

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Logic of Hypothesis Testing There are three equivalent ways to perform a hypothesis test They will reach the same conclusion The methods are The classical approach The P -value approach The confidence interval approach
Logic of Hypothesis Testing The classical approach If the sample value is too many standard deviations away, then it must be too unlikely If the sample value is too many standard deviations away, then it must be too unlikely The P -value approach If the probability of the sample value being that far away is small, then it must be too unlikely The confidence interval approach If we are not sufficiently confident that the parameter is likely enough, then it must be too unlikely Don’t worry … we’ll be explaining more

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Logic of Hypothesis Testing The three methods all begin the same way We have a null hypothesis, that the actual mean is equal to a value μ 0 We have an alternative hypothesis We have a null hypothesis, that the actual mean is
Logic of Hypothesis Testing The three methods all need information We run an experiment We collect the data We calculate the sample mean We run an experiment We collect the data We calculate the sample mean The three methods all make the same assumptions to be able to make the statistical calculations That the sample is a simple random sample That the sample mean has a normal distribution

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Logic of Hypothesis Testing In this section we assume that the population standard deviation σ is known (as in section 9.1) We can apply our techniques if either The population has a normal distribution, or Our sample size n is large ( n ≥ 30) In those cases, the distribution of the sample mean is normal with mean μ and standard deviation σ / √ n x
Logic of Hypothesis Testing The three methods all compare the observed results with the previous criterion

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