Introduction to Probability and Statistics for Engineers and Scientists

260 Chapter 7: Parameter Estimation

The 95% lower confidence interval for the mean difference is (2.4971, infinity)

Confidence Interval: Unknown but Equal Variances

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(b)

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One-Sided

Two-Sided

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Enter the value of a:

(0 < a < 1)

.05

Data value = 135

Data value = 142

152

144

132

142

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154

136

142

List 1 Sample size = 12

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List 2 Sample size = 14 134

130

146

128

131

137

135

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FIGURE 7.5 (continued)

which, by our previous analysis, has at-distribution withn+m−2 degrees of freedom.
The results of this section are summarized up in Table 7.2.

7.5 APPROXIMATE CONFIDENCE INTERVAL FOR THE

MEAN OF A BERNOULLI RANDOM VARIABLE

Consider a population of items, each of which independently meets certain standards with
some unknown probabilityp.Ifnof these items are tested to determine whether they meet
the standards, how can we use the resulting data to obtain a confidence interval forp?
If we letXdenote the number of thenitems that meet the standards, thenXis a
binomial random variable with parametersnandp. Thus, whennis large, it follows by