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# Computing Confidence Interval Mean

Computing Confidence Interval Mean. Fictitious Stress Index (FSI).

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## Computing Confidence Interval Mean

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1. Computing Confidence Interval Mean

2. Fictitious Stress Index (FSI) The Fictitious Stress Index (FSI) is a measure of a person's stress level. The FSI ranges from 0 to 70. A researcher acquires a random sample of undergraduates at Kennesaw State University, and administers the FSI to these students at the beginning of Fall Semester 2000. The FSI scores follow: • 8 8 9 10 11 14 17 19 20 • 22 24 25 26 27 27 28 29 29 • 30 32 32 33 34 35 35 36 38 • 40 40 42 44 46 52 58 66

3. Mean Stress Level We wish to estimate the population mean FSI for undergraduates at Kennesaw State University.

4. Sample Statistics

5. Our next step is to select a confidence level this number will provide a level of confidence in our estimation process. A standard choice is 95% confidence. Using the table @ http://www.mindspring.com/~cjalverson/ztable.htm, we obtain the following row: 2.00 0.022750 0.95450 Our multiplier is 2.00. Confidence Level

6. Lower Confidence Bound n = 39 m ≈ 27.6923 sd  14.6631 Z = 2 lower bound = m – Z*sd/(n) ≈ 27.6923 – 2*14.6631/(39) ≈ 22.9963

7. Upper Confidence Bound n = 39 m ≈ 27.6923 sd  14.6631 Z = 2 upper bound = m + Z*(sd/n) ≈ 27.6923 + 2*(14.6631/39) ≈ 32.3882

8. Write the Interval We write the approximate interval as [22.9963,32.3882].

9. Confidence Estimation Schematic Compute lower = m – Z*(sd/n) upper = m + Z*(sd/n) Compute m sd Population  Obtain Sample Size = n

10. Interpretation ─ Population and Mean We seek the population mean Fictitious Stress Index for undergraduates at Kennesaw State University.

11. Interpretation ─ Family of Samples We obtain random samples of n=39 students per sample. Our Family of Samples consists of every possible random sample as described above.

12. Interpretation ─ Family of Intervals From each member of the Family of Samples we comupute the interval [m - 2(sd/n), m + 2(sd/n)]. Our Family of Intervals consists of every possible interval computed as above.

13. Interpretation ─ Confidence Approximately 95% of the members of the Family of Intervals cover , the population mean Fictitious Stress Index for undergraduates at Kennesaw State University. The remaining 5% or so fail. We view our single interval, [22.9968,32.3882]., as being drawn at random from the Family of Intervals. If our interval is drawn from the 95% supermajority, then the population mean Fictitious Stress Index for undergraduates at Kennesaw State University is between 22.9968 and 32.3882 .

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