Transcript Confidence Intervals for the Mean (Large Samples)

Confidence Intervals
STATISTIK
LECTURE:
AL MUIZZUDDIN F., SE., ME.
Confidence Intervals for the Mean
(Large Samples)
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• 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 or
underestimate the population parameter.
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• 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 THE
POPULATION 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
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