APPENDIX D Key Formulas A33 CHAPTER 6 c-Confidence Interval for m: x - E 6 m 6 x + E, where E = zc s2 n when s is known, the sample is random, and either the population is normally distributed or n Ú 30, or E = tc s2 n when s is unknown, the sample is random, and either the population is normally distributed or n Ú 30. If the distribution of a random variable x is approximately normal, then t = x - m s 1n follows a t-distribution. Minimum Sample Size to Estimate m: n = a zcs E b 2 Point Estimate for p, the population proportion of successes: pn = x n c-Confidence Interval for Population Proportion p (when np Ú 5 and nq Ú 5): pn - E 6 p 6 pn + E, where E = zcApnqn n Minimum Sample Size to Estimate p: n = pnqna zc Eb 2 If a random variable x has a normal distribution, then the distribution of x 2 = 1n - 12s2 s 2 forms a chi-square distribution for samples of any size n 7 1. c-Confidence Interval for Population Variance s 2: (n - 1)s2 x 2 R 6 s 2 6 (n - 1)s2 x 2 L c-Confidence Interval for Population Standard Deviation s: A(n - 1)s2 x 2 R 6 s 6 A(n - 1)s2 x 2 L CHAPTER 7 z-Test for a Mean m: z = x - m s/2n , when s is known, the sample is random, and either the population is normally distributed or n Ú 30. t-Test for a Mean m: t = x - m s/2n , when s is unknown, the sample is random, and either the population is normally distributed or n Ú 30. (d.f. = n - 1) z-Test for a Proportion p (when np Ú 5 and nq Ú 5): z = pn - mpn spn = pn - p 2 pq/n Chi-Square Test for a Variance s 2 or Standard Deviation s: x 2 = (n - 1)s2 s 2 (d.f. = n - 1)
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