use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. of 346 items tested, 12 are found to be defective. construct the 98% confidence interval for the proportion of all such items that are defective.

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12-12-2022
Mathematics

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use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. of 346 items tested, 12 are found to be defective. construct the 98% confidence interval for the proportion of all such items that are defective.

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contexto1019 contexto1019 · Answer 1 · 2022-12-22T20:31:51-05:00

The 98% confidence interval for the population proportion p of defective items is (0.0287, 0.0403).

To construct a 98% confidence interval for the population proportion p of defective items, we can use the formula p ± 2 √ (p(1 - p)) / n, where p is the sample proportion of defective items (12/346 = 0.0345), n is the sample size (346), and 2 is the critical value for a 98% confidence interval (corresponding to a Z-score of 2). Substituting these values into the formula gives us 0.0345 ± 0.0058, so the 98% confidence interval for the population proportion p of defective items is (0.0287, 0.0403). This interval represents the range of values for p that we can be 98% confident contain the true population proportion of defective items.

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