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Estimasi Parameter TIP-FTP-UB

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Statistika Inferensial Terbagi dua bagian: Estimasi (estimation) Uji hipotesis (test of hypotheses)

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Estimasi Terbagi menjadi dua bagian: Estimasi titik Estimasi interval

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10.4 Point & Interval Estimation… For example, suppose we want to estimate the mean summer income of a class of business students. For n=25 students, mean income is calculated to be 400 $/week. point estimate interval estimate An alternative statement is: The mean income is between 380 and 420 $/week.

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Estimator

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Estimasi titik Sebuah nilai tunggal yang digunakan untuk mengestimasi sebuah parameter disebut titik estimator (atau cukup estimator), sedangkan proses untuk mengestimasi titik disebut estimasi titik (point estimation).

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Estimasi Titik

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Estimasi Interval

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Four commonly used confidence levels… Confidence Level cut & keep handy! Table 10.1

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Example 1 A computer company samples demand during lead time over 25 time periods: It is known that the standard deviation of demand over lead time is 75 computers. We want to estimate the mean demand over lead time with 95% confidence in order to set inventory levels…

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Example 1 IDENTIFY

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Example 1 In order to use our confidence interval estimator, we need the following pieces of data: therefore: The lower and upper confidence limits are and n 25 Given Calculated from the data…

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Interval Width… A wide interval provides little information. For example, suppose we estimate with 95% confidence that an accountant’s average starting salary is between $15,000 and $100,000. Contrast this with: a 95% confidence interval estimate of starting salaries between $42,000 and $45,000. The second estimate is much narrower, providing accounting students more precise information about starting salaries.

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Interval Width… The width of the confidence interval estimate is a function of the confidence level, the population standard deviation, and the sample size…

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Interval Width The width of the confidence interval estimate is a function of the confidence level, the population standard deviation, and the sample size A larger confidence level produces a w i d e r confidence interval:

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Interval Width… The width of the confidence interval estimate is a function of the confidence level, the population standard deviation, and the sample size… Larger values of produce w i d e r confidence intervals

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Interval Width The width of the confidence interval estimate is a function of the confidence level, the population standard deviation, and the sample size Increasing the sample size decreases the width of the confidence interval while the confidence level can remain unchanged. Note: this also increases the cost of obtaining additional data

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Selecting the Sample Size We can control the width of the interval by determining the sample size necessary to produce narrow intervals. Suppose we want to estimate the mean demand “to within 5 units”; i.e. we want to the interval estimate to be: Since: It follows that

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Selecting the Sample Size Solving the equation that is, to produce a 95% confidence interval estimate of the mean (±5 units), we need to sample 865 lead time periods (vs. the 25 data points we have currently).

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Sample Size to Estimate a Mean The general formula for the sample size needed to estimate a population mean with an interval estimate of: Requires a sample size of at least this large:

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Example 2 A lumber company must estimate the mean diameter of trees to determine whether or not there is sufficient lumber to harvest an area of forest. They need to estimate this to within 1 inch at a confidence level of 99%. The tree diameters are normally distributed with a standard deviation of 6 inches. How many trees need to be sampled?

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Example 2 Things we know: Confidence level = 99%, therefore =.01 We want, hence W=1. We are given that = 6. 1

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Example 2 We compute That is, we will need to sample at least 239 trees to have a 99% confidence interval of 1

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