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8.1 Estimation Using Normal

# 8.1 Estimation Using Normal - Outcome 8.1 Know how to...

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Interval Estimation INTERVAL ESTIMATION BUQU 1230 Esther Tiessen Outcome 8.1— Know how to construct and interpret an interval estimate of a population mean when the population standard deviation is known.

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Interval Estimation Interval Estimation Population Mean: σ Known Population Mean: σ Unknown Population Proportion
Interval Estimation Population Mean: σ Known σ known in some cases: standard deviation may be known, even if population mean is unknown relevant historic data may be available in quality control circumstances, if process is assumed to be operating correctly

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Interval Estimation σ Known Example Oxford Cereals fills thousands of boxes of cereal during an 8-hour shift. The be consistent with package labeling, boxes should contain a mean of 368 grams of cereal. Because of the speed of the process, the cereal weight varies from box to box, causing some boxes to be underfilled and others overfilled (the standard deviation is known to be 0.15 grams). If the process is not working properly, the mean weight in the boxes could vary too much from the label weight of 368 grams to be acceptable. Because weighing every box is too costly, a sample of boxes is selected. The sample is used to decide whether to maintain, alter, or shut down the cereal-filling process.
Interval Estimation σ Known Example Oxford Cereals fills thousands of boxes of cereal during an 8-hour shift. The be consistent with package labeling, boxes should contain a mean of 368 grams of cereal. Because of the speed of the process, the cereal weight varies from box to box, causing some boxes to be underfilled and others overfilled (the standard deviation is known to be 0.15 grams). If the process is not working properly, the mean weight in the boxes could vary too much from the label weight of 368 grams to be acceptable. Because weighing every box is too costly, a sample of boxes is selected. The sample is used to decide whether to maintain, alter, or shut down the cereal-filling process. No way to determine the population mean —use a sample to make inference about population mean.

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Interval Estimation σ Known Example Oxford Cereals fills thousands of boxes of cereal during an 8-hour shift. The be consistent with package labeling, boxes should contain a mean of 368 grams of cereal. Because of the speed of the process, the cereal weight varies from box to box, causing some boxes to be underfilled and others overfilled (the standard deviation is known to be 0.15 grams). If the process is not working properly, the mean weight in the boxes could vary too much from the label weight of 368 grams to be acceptable. Because weighing every box is too costly, a sample of boxes is selected. The sample is used to decide whether to maintain, alter, or shut down the cereal-filling process.
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