# Statistics Test 4 Formula Sheet (Notes).docx - Unit 4...

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Unit 4 – Inferential Statistics Estimator A strategy or rule used to approximate the value of a population parameter Point Estimate = A single value e.g. x estimates μ s 2 estimates σ 2 ^ p estimates p Unbiased estimators Expected Value = Parameter Interval Estimate A range of values likely to contain the parameter Mean Squared Error Difference between the estimate and the parameter. Choose a tolerable amount of error. Use the statistic’s distribution. e.g. Sample Means If CLT assumptions are met, x will be normal. 95% confidence 5% “uncertainty” Confidence Interval For Normal Distributions (Point Estimate) ± (Margin of Error) Margin of Error E = (Critical Value) × (Standard Error) 95% = 0.95 0.95 2 = 0.4750 To find normal critical values, 1. Confidence Level 2 2. Use Table C “backwards” to find z corresponding to the area. Confidence Level = 1 – α α = 1 – Confidence α = “uncertainty” or tolerable error Critical Value = z α / 2 Confidence Interval to Estimate μ Assumption: CLT, σ known 1. Find x and σ 2. Find z α / 2 for confidence level Intervals for Means
A sample of 106 hospital patients has a mean body temperature of 98.20 and σ is known to be 0.62 . Estimate the population mean using the 90% and 99% confidence intervals. α z α 4. 98.20 0.16 ≤μ≤ 98.20 + 0.1698.04 ≤ μ≤ 98.36
e.g. Confidence Intervals for Means A sample of 50 quarters has a mean weight of 5.622 g and σ = 0.068 g. Find the 98% confidence interval for the mean weight of a quarter. σ / 2 E e.g. A foundry that manufactures steel bars tests 11 bars of a new alloy. The average breaking strength is 43.7 tons with s = 24.4 tons. Find the 95% confidence interval for the
mean breaking strength of the new material. Assume a bell-shaped distribution. 2 α