MATH117_Lecture_Lock5-2 - Section 5.2 Confidence Intervals and P-values using Normal Distributions Statistics Unlocking the Power of Data Lock5 Outline

MATH117_Lecture_Lock5-2 - Section 5.2 Confidence Intervals...

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Statistics: Unlocking the Power of Data Lock 5 Section 5.2 Confidence Intervals and P-values using Normal Distributions
Statistics: Unlocking the Power of Data Lock 5 Outline Central limit theorem Confidence interval using a normal distribution Hypothesis test using a normal distribution
Statistics: Unlocking the Power of Data Lock 5 Central Limit Theorem For random samples with a sufficiently large sample size, the distribution of sample statistics for a mean or a proportion is normally distributed
Statistics: Unlocking the Power of Data Lock 5 slope ( thousandths ) -60 -40 -20 0 20 40 60 Dot Plot r -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 Nullxbar 98.2 98.3 98.4 98.5 98.6 98.7 98.8 98.9 99.0 Dot Plot Diff -4 -3 -2 -1 0 1 2 3 4 xbar 26 27 28 29 30 31 32 Dot Plot Slope :Restaurant tips Correlation: Malevolent uniforms Mean :Body Temperatures Diff means: Finger taps Mean : Atlanta commutes phat 0.3 0.4 0.5 0.6 0.7 0.8 Proportion : Owners/dogs Bootstrap and Randomization Distributions
Statistics: Unlocking the Power of Data Lock 5 Central Limit Theorem The central limit theorem holds for ANY original distribution, although “sufficiently large sample size” varies The more skewed the original distribution is, the larger n has to be for the CLT to work For quantitative variables that are not very skewed, n ≥ 30 is usually sufficient For categorical variables, counts of at least 10 within each category is usually sufficient
Statistics: Unlocking the Power of Data Lock 5 Hearing Loss In a random sample of 1771 Americans aged 12 to 19, 19.5% had some hearing loss (this is a

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