SlideServe
Télécharger Obtenir Pro
Menu
Accueil Pro
Préférences
ApparenceLight Aide et commentaires
© SlideServe · v2026

Estimating the Proportion of Red Marbles Using Confidence Intervals

mead avatar
mead
15 diapositives · 274 Views · Oct 22, 2014

This guide demonstrates how to estimate the population proportion of red marbles in a bowl containing marbles of three colors: red, green, and blue. By using a sample of marbles, we apply statistical methods to compute the sample proportion and standard deviation. We set a confidence level of 95%, utilizing a z-score to calculate the confidence interval for the true proportion of red marbles. We derive an interval of approximately [0.1703, 0.4296], indicating that we are 95% confident the true proportion of red marbles falls within this range.

#estimating the proportion of red marbles using confidence intervals #estimating the proportion of red marbles using confidence intervals ppt #powerpoint #presentation
Estimating the Proportion of Red Marbles Using Confidence Intervals - slide 1
01 / 15Estimating the Proportion of Red Marbles Using Confidence Intervals
1 / 17

Télécharger la présentation

Estimating the Proportion of Red Marbles Using Confidence Intervals
Une image / un lien ci-dessous est fourni (tel quel) pour télécharger la présentation

Politique de téléchargement : le contenu du site vous est fourni TEL QUEL pour votre information et votre usage personnel ; il ne peut être vendu, concédé sous licence ni partagé sur d’autres sites sans l’accord de son auteur.Le contenu vous est fourni TEL QUEL, pour votre information et votre usage personnel uniquement. Téléchargez la présentation en cliquant sur ce lien. Lors du téléchargement, si vous ne parvenez pas à télécharger une présentation, l’éditeur a peut-être supprimé le fichier de son serveur.Pendant le téléchargement, si vous ne parvenez pas à obtenir une présentation, le fichier a peut-être été supprimé par l’éditeur.

F I N

Plus de contenu associé

Transcription de la présentation

  1. Computing Confidence Interval Proportion

  2. A Three Color Bowl Suppose we have a bowl containing marbles, each identical in size, texture and weight, in three colors: Red, Green, Blue.

  3. Proportion Red Suppose we have a large population containing marbles, each identical in size, texture and weight, in three colors: Red, Green, Blue. Suppose further that we wish to estimate the population proportion of red, but that examining the population directly and exhaustively is impractical.

  4. Sample Proportion Red

  5. Sample Proportion Red nred = 15 n = 20 + 15 + 15 = 50 pred = 15 / n = 15 / 50 = .30 sdp = sqrt(p*(1-p)/n) = sqrt(.30*(1-p)/n) = sqrt(.30*.70/n) = sqrt(.30*.70/50) = sqrt(.210/50) ≈ sqrt(.0042)  .06481

  6. 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

  7. Lower Confidence Bound pred = .30 sdp  .06481 Z = 2 lower bound = pred – Z*sdp = .30 – Z*sdp = .30 ─ 2*sdp ≈ .30 ─ 2*.06481 ≈ .30 ─ 2*.06481 ≈ .1703

  8. Upper Confidence Bound pred = .30 sdp  .06481 Z = 2 upper bound = pred + Z*sdp = .30 + Z*sdp = .30 +2*sdp ≈ .30 + 2*.06481 ≈ .30 + 2*.06481 ≈ .4296

  9. Write the Interval We write the approximate interval as [.1703, .4296].

  10. Confidence Estimation Schematic Compute lower = pred – Z*sdp upper = pred + Z*sdp Compute nred pred sdp Population Pred Obtain Sample Size = n

  11. Interpretation ─ Population and Proportion We have a large population of marbles. We seek the true population proportion of red marbles for this population.

  12. Interpretation ─ Family of Samples We obtain random samples of n=50 marbles per sample. Each marble is drawn from the population with replacement. Our Family of Samples consists of every possible random sample as described above.

  13. Interpretation ─ Family of Intervals From each member of the Family of Samples we comupute the interval [pred─ 2*sdp, pred+ 2*sdp]; where pred = nred/n, and sdp=sqrt(pred*(1- pred)/n). Our Family of Intervals consists of every possible interval computed as above.

  14. Interpretation ─ Confidence Approximately 95% of the members of the Family of Intervals cover Pred, the true population proportion of red marbles. The remaining 5% or so fail. We view our single interval, [.1703, .4296], as being drawn at random from the Family of Intervals. If our interval is drawn from the 95% supermajority, then between 17.03% and 42.96% of the marbles are red.