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Ch 6 Introduction to Formal Statistical Inference

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6.1 Large Sample Confidence Intervals for a Mean A confidence interval for a parameter is a data-based interval of numbers likely to include the true value of the parameter with a probability-based confidence. A 95% confidence interval for µ is an interval which was constructed in a manner such that 95% of such intervals contain the true value of µ.

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Interval Estimate—Confidence intervals An interval estimate consists of an interval which will contain the quantity it is supposed to estimate with a specified probability (or degree of confidence). Recall that for large random samples from infinite populations, the sampling distribution of the mean is approximately a normal distribution with So we will utilize some properties of normal distribution to explain a confidence interval.

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For a standard normal curve

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Large-sample known confidence interval for

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Confidence Intervals 100(1-a)% CI: 80% 90% 95% 99%

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Confidence Interval for Means After computing sample mean, find a range of values such that 95% of the time the resulting range includes the true value .

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X=breaking strength of a fish line. σ=0.10. In a random sample of size n=10, Find a 95% confidence interval for μ, the true average breaking strength.

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How large a sample size is needed in order to get an error of no more than 0.01 with 95% probability if the sample mean is used to estimate the true mean? Solution n=385, always round up!

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