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Transcript

CONFIDENCE INTERVAL for the mean unknown mean of the population known standard deviation size of a random sample mean of the random sample ̅ Compute an interval with high probability of containing . Choose a number , such as 0.01, 0.05, or 0.1, the interval will have 100( )% chance of containing , such as 99%, 95% or 90%. ⁄ corresponding to the In the standard normal table look up the z-value, ⁄ . If you also have a table of upper percentages you may find probability ⁄ , corresponding to ⁄ in this table. See the figure below for the z-value a visual description: area area area 0 As ̅ , , , and containing is: are known, the confidence interval with probability of ̅ ( ) √ ̅ ( ) √ of CONFIDENCE INTERVAL for a difference of means One way to compare populations would be to look at the difference of their means. Let ̅ ̅ mean of random sample of size mean of random sample of size from one population, and from another population. The means of the populations, and are unknown so it is necessary to calculate a confidence interval for their difference . Choose small , so that the confidence interval will have a probability containing . of Find If the standard deviation, 1 and 2, of the two populations are known, then The confidence interval with the probability ̅ ̅ ( )√ ̅ of containing ̅ is: ( )√ If the standard deviations, and , of the two populations are unknown and the sample sizes are large enough, the calculated variances and can be substituted for and , respectively.