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Advance Algebra Unit One – Data Analysis

Advance Algebra Unit One – Data Analysis. Estimating Population Mean. Terms. Sample Mean Sample Standard Deviation Number in Sample Standard Error of Mean Z-score Confidence Interval. Problem.

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Advance Algebra Unit One – Data Analysis

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  1. Advance AlgebraUnit One – Data Analysis Estimating Population Mean

  2. Terms Sample Mean Sample Standard Deviation Number in Sample Standard Error of Mean Z-score Confidence Interval

  3. Problem You have a sample from a population you are studying. You want to know how close the mean of your sample is to the population mean. Find the Confidence Interval

  4. Example A sample of 30 pieces of data from a population has a mean of 45 and a standard deviation of 5. Find a interval estimate with a confidence interval of 95%.

  5. Step One Find number in the sample, sample mean and sample deviation Sample Mean: 45 Sample Deviation : 5 Number in sample: 30

  6. Step Two Find Standard (Margin of) Error of the Mean SEM = Sample Deviation √Number in Sample SEM = 5/√30 = .913

  7. Step Three Find the Z-scores 95% 95/2 = 47.5 50 – 47.5 = 2.5% 50 + 47.5 = 97.5% Z-score for .025 = -1.96 Z-score for .975 = 1.96

  8. Confidence Interval Interval = Sample Mean ± z-score (Standard Error of the Mean) Interval = 45 ± 1.96(.913) Interval = 43.21, 46.79

  9. Example A sample of 20 pieces of data from a population has a mean of 30 and a standard deviation of 2. Find a interval estimate with a confidence interval of 95%.

  10. Step One Find number in the sample, sample mean and sample deviation Sample Mean: 30 Sample Deviation : 2 Number in sample: 20

  11. Step Two Find Standard Error of the Mean SEM = Sample Deviation √Number in Sample SEM = 2/√20 = .447

  12. Step Three Find the Z-scores 95% 95/2 = 47.5 50 – 47.5 = 2.5% 50 + 47.5 = 97.5% Z-score for .025 = -1.96 Z-score for .975 = 1.96

  13. Confidence Interval Interval = Sample Mean ± z-score (Standard Error of the Mean) Interval = 30 ± 1.96(.447) Interval = 29.12, 30.88

  14. Example A sample of 40 pieces of data from a population has a mean of 115 and a standard deviation of 12. Find a interval estimate with a confidence interval of 99%.

  15. Step One Find number in the sample, sample mean and sample deviation Sample Mean: 115 Sample Deviation : 12 Number in sample: 40

  16. Step Two Find Standard Error of the Mean SEM = Sample Deviation √Number in Sample SEM = 12/√40 = 1.897

  17. Step Three Find the Z-scores 99% 99/2 = 49.5 50 – 49.5 =.5% 50 + 49.5 = 99.5% Z-score for .005 = -2.575 Z-score for .995 = 2.575

  18. Confidence Interval Interval = Sample Mean ± z-score (Standard Error of the Mean) Interval = 115 ± 2.575(1.897) Interval = 110.12, 119.88

  19. Margin of Error Half the distance of your confidence interval Or High end score – Mean

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