STATISTIKLECTURE:

AL MUIZZUDDIN F., SE., ME.

Confidence Intervals

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Confidence Intervals for the Mean (Large Samples)

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Next

• In this chapter, you will learn an important technique of statistical inference—to use sample statistics to estimate the value of an unknown population parameter.

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Next

• In this section, you will learn how to use sample statistics to make an estimate of the population parameter when the sample size is at least 30 or when the population is normally distributed and the standard deviation is known. To make such an inference, begin by finding a point estimate.

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A statistic is unbiased if it does not overestimate orunderestimate the population parameter.

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Next

• In Example 1, the probability that the population mean is exactly 130.8 is virtually zero. So, instead of estimating to be exactly 130.8 using a point estimate, you can estimate that lies in an interval. This is called making an interval estimate.

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Before finding a margin of error for an interval estimate, you should first determine how confident you need to be that your interval estimate contains the population mean

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CONFIDENCE INTERVALS FOR THEPOPULATION MEAN

• Using a point estimate and a margin of error, you can construct an interval estimate of a population parameter. This interval estimate is called a confidence interval.

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SAMPLE SIZE

• For the same sample statistics, as the level of confidence increases, the confidence interval widens. As the confidence interval widens, the precision of the estimate decreases.

• One way to improve the precision of an estimate without decreasing the level of confidence is to increase the sample size.

• But how large a sample size is needed to guarantee a certain level of confidence for a given margin of error?

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Latihan Soal

• Construct the 90% and 95% confidence intervals for the population mean.

• Interpret the results and compare the widths of the confidence intervals.

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Latihan Soal

1. A random sample of 34 home theater systems has a mean price of $452.80 and a standard deviation of $85.50.

2. From a random sample of 48 days in a recent year, U.S. gasoline prices had a mean of $2.34 and a standard deviation of $0.32.

3. A random sample of 31 eight-ounce servings of different juice drinks has a mean of 99.3 calories and a standard deviation of 41.5 calories.

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Next, no.4

• A machine cuts plastic into sheets that are 50 feet (600 inches) long.Assume that the population of lengths is normally distributed. The company wants to estimate the mean length of the sheets within 0.125 inch.

• Determine the minimum sample size required to construct a 95% confidence interval for the population mean. Assume the population standard deviation is 0.25 inch.

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Tugas

• Kerjakan soal latihan case study: hal 317 Larson, 2012

• Minggu depan dikumpulkan.

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•SELESAI