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A textile manufacturer wants to set up a control chart for irregularities (e.g., oil stains, shop soil, loose threads, and tears) per 100 square yards of carpet. The following data were collected from a sample of twenty 100-square-yard pieces of carpet Cbar= 10.25
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6 gru 2020 · In Inference for One Proportion, we are estimating the population proportion p. So we estimate the standard error by replacing p with the sample proportion, which affects the margin of error in the confidence interval.
Estimating a population proportion \(p\) The sample size necessary for estimating a population proportion \(p\) of a large population with ((1-\alpha)100\%\) confidence and error no larger than \(\epsilon\) is: \(n=\dfrac{z^2_{\alpha/2}\hat{p}(1-\hat{p})}{\epsilon^2}\)
To form a proportion, take X, the random variable for the number of successes and divide it by n, the number of trials (or the sample size). The random variable P′ (read “P prime”) is that proportion, (Sometimes the random variable is denoted as , read “P hat”.)
A textile manufacturer wants to set up a control chart for irregularities (e.g., oil stains, shop soil, loose threads, and tears) per 100 square yards of carpet. The following data were collected from a sample of twenty 100-square-yard pieces of carpet:
To form a proportion, take X, the random variable for the number of successes and divide it by n, the number of trials (or the sample size). The random variable P′ (read “P prime”) is that proportion, P ′ = X n P ′ = X n. (Sometimes the random variable is denoted as ^P P ^, read “P hat”.)
