Class Notes 10

# Class Notes 10 - 7.3 How Can We Construct a Confidence...

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7.3: How Can We Construct a Confidence Interval to Predict a Population Mean One-sample z Confidence Interval for μ: The general formula for a confidence interval for a population mean μ when 1. x = is the sample mean from a random sample . 2. the sample size n is lar ge (generally n ≥ 30), and 3. σ, the population standard deviation , is known is ( 29 x z critical value n σ ± This interval can also be used if n is small (generally n < 30) but it is reasonable to believe that the distribution of values in the population is normal. Filling Machine: A certain filling machine has a true population standard deviation σ = 0.228 ounces when used to fill catsup bottles. A random sample of 36 “6 ounce” bottles of catsup was selected from the output from this machine and the sample mean was 6.018 ounces. Find a 90% confidence interval estimate for the true mean fills of catsup from this machine. Unknown σ - Small Size Samples [All Size Samples] t distribution: If X is a normally distributed random variable, the statistic / x t s n μ - = follows a t distribution with df = n-1 (degrees of freedom). This statistic / x t s n - = is fairly robust and the results are reasonable for moderate sample sizes (15 and up) if x is just reasonable centrally weighted. It is also quite reasonable for large sample sizes for

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Class Notes 10 - 7.3 How Can We Construct a Confidence...

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