8.1 Estimation Using Normal

# Population distribution normal distribution mean

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## This document was uploaded on 03/05/2014.

Ask a homework question - tutors are online