Introduction to Probability and Statistics for Engineers and Scientists
244 Chapter 7: Parameter Estimation Hence, a 100(1−α) percent two-sided confidence interval forμis ( x−zα/2 σ √ n , x+zα/2 σ √ n ...
7.3Interval Estimates 245 Sometimes we are interested in a two-sided confidence interval of a certain level, say 1 −α, and the p ...
246 Chapter 7: Parameter Estimation Because the estimatexis within 1.96(σ/ √ n)=.588/ √ nof any point in the interval, it follow ...
7.3Interval Estimates 247 Area = a/2 ta/2, n–1 t Area = a/2 –ta/2, n–1 P{–ta/2,n–1< Tn–1 < ta/2,n–1} = 1 – a FIGURE 7.2 t- ...
248 Chapter 7: Parameter Estimation and our estimate of it turned out to be 9.5, which resulted in a larger confidence interval. ...
7.3Interval Estimates 249 or P { X−μ< S √ n tα,n− 1 } = 1 −α or P { μ>X− S √ n tα,n− 1 } = 1 −α Hence, if it is observed t ...
250 Chapter 7: Parameter Estimation The 95% confidence interval for the mean is (60.865, 77.6683) Confidence Interval: Unknown V ...
7.3Interval Estimates 251 Now, the values of independent uniform (0, 1) random variables can be approximated on a computer (by s ...
252 Chapter 7: Parameter Estimation Hence whenS^2 =s^2 , a 100(1−α) percent confidence interval forσ^2 is { (n−1)s^2 χα^2 /2,n− ...
7.4Estimating the Difference in Means of Two Normal Populations 253 it follows that, with confidence .90, σ^2 ∈(7.267× 10 −^6 , ...
254 Chapter 7: Parameter Estimation or, equivalently, P X−Y−zα/2 √ σ 12 n + σ 22 m <μ 1 −μ 2 <X−Y+zα/2 √ σ 12 n + σ 2 ...
7.4Estimating the Difference in Means of Two Normal Populations 255 The 95% confidence interval for the mean is (-19.6056, -6.48 ...
256 Chapter 7: Parameter Estimation The 95% lower confidence interval for the mean is (-infinity, -7.544) Confidence Interval: T ...
7.4Estimating the Difference in Means of Two Normal Populations 257 are equal and letσ^2 denote their common value. Now, from Th ...
258 Chapter 7: Parameter Estimation Therefore, when the data result in the valuesX =x,Y =y,Sp=sp, we obtain the following 100(1− ...
7.4Estimating the Difference in Means of Two Normal Populations 259 the estimator ofσ^2 is thepooled estimator Sp^2 = (n−1)S 12 ...
260 Chapter 7: Parameter Estimation The 95% lower confidence interval for the mean difference is (2.4971, infinity) Confidence I ...
7.5Approximate Confidence Interval for the Mean of a Bernoulli Random Variable 261 TABLE 7.2 100(1−σ)Percent Confidence Interval ...
262 Chapter 7: Parameter Estimation pˆ is the maximum likelihood estimator ofp, and so should be approximately equal top. As a r ...
7.5Approximate Confidence Interval for the Mean of a Bernoulli Random Variable 263 wherenis the size of the sample. Since the “m ...
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