Population distribution normal distribution mean

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Unformatted text preview: s normal distribution): Interval Estimation Sample mean = 362.3 grams (given in problem) CONFIDENCE(0.05,15,2 Standard error of the mean: σ =σ = 3 x 2 5 Confidence Interval 5) ◦ . 3. 9 8 margin of error is 5.88: z σ z531 ⋅ = 8 α x=02 = 6 5 2 0 . ◦ therefore, interval is ◦ 3 23 58 6. ± . 8 Interval Estimate 3 64 ≤µ 3 81 5. 2 ≤ 6. 8 Given a sample mean of 362.3, we can be 95% confident that the population mean is between 356.42 and 368.18 grams. σ Known Example If the sample mean is found to be 362.3, find the 95% confidence interval (i.e., interval estimate) for the population mean. Population distribution: ◦ Normal distribution: Mean μ = ? grams—determine interval estimate Standard deviation σ = 15 grams Sampling distribution for Sample Size n = 25: ◦ Normal distribution (population follows normal distribution): Interval Estimation Sample mean = 362.3 grams (given in problem) CONFIDENCE(0.05,15,2 Standard error of the mean: σ =σ = 3 x 2 5 5) 362.3 – Confidence Interval CONFIDENCE(0.05,15,25) ◦ . 3. 9 8 margin of error is 5.88: z σ z531 ⋅ = 8 α x=02 = 6 5 2 0 . ◦ ◦ therefore, interval is 3 23 58 6. ± . 8 Interval Estimate 3 64 ≤µ 3 81 5. 2 ≤ 6. 8 Given a sample mean of 362.3, we can be 95% confident that the 362.3 + population mean is between 356.42 and 368.18 grams. CONFIDENCE(0.05,15,25) σ Known Example Interval estimate for population mean given sample 3 4 ≤8 6 ≤ 31 . . mean of 362.3: 5 2µ 68 Interval Estimation σ Known Example Interval estimate for population mean given sample 3 4 ≤8 6 ≤ 31 . . mean of 362.3: 5 2µ 68 can choose another sample and calculate another sample mean: e.g., 369.5 ◦ 3 95± .8 6. 5 8 3 36 ≤µ 3 53 6. 2 ≤ 7. 8 New interval estimate: Interval Estimation σ Known Example Interval estimate for population mean given sample 3 4 ≤8 6 ≤ 31 . . mean of 362.3: 5 2µ 68 can choose another sample and calculate another sample mean: e.g., 369.5 3 95± .8 6. 5 8 3 36 ≤µ 3 53 6. 2 ≤ 7. 8 ◦ New interval estimate: ◦ If μ=368, this interval estimate is also true. Interval Estimation σ Known Example Interval estimate for population mean given sample 3 4 ≤8 6 ≤ 31 . . mean of 362.3: 5 2µ 68 can choose another sample and...
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This document was uploaded on 03/05/2014.

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