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Point Estimate

Point Estimate. DEFINITION: A point estimate is a single value estimate for a population parameter. The best point estimate of the population mean is the sample mean. Example: Point Estimate .

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Point Estimate

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  1. Point Estimate DEFINITION: A point estimate is a single value estimate for a population parameter. The best point estimate of the population mean is thesample mean

  2. Example: Point Estimate A random sample of 35 airfare prices (in dollars) for a one-way ticket from Atlanta to Chicago. Find a point estimate for the population mean, . 99 101 107 102 109 98 105 103 101 105 98 107 104 96 105 95 98 94 100 104 111 114 87 104 108 101 87 103 106 117 94 103 101 105 90 The sample mean is The point estimate for the price of all one way tickets from Atlanta to Chicago is $101.77.

  3. Interval Estimates • • 101.77 101.77 ) ( Point estimate An interval estimate is an interval or range of values used to estimate a population parameter. The level of confidence, x, is the probability that the interval estimate contains the population parameter.

  4. Distribution of Sample Means When the sample size is at least 30, the sampling distribution for is normal. Sampling distributionof For c = 0.95 0.95 0.025 0.025 z -1.96 0 1.96 95% of all sample means will have standard scores between z = -1.96 and z = 1.96

  5. Maximum Error of Estimate The maximum error of estimate E is the greatest possible distance between the point estimate and the value of the parameter it is, estimating for a given level of confidence, c. When n 30, the sample standard deviation, s, can be used for . Find E, the maximum error of estimate for the one-way plane fare from Atlanta to Chicago for a 95% level of confidence given s = 6.69. Using zc= 1.96, s = 6.69, and n = 35, You are 95% confident that the maximum error of estimate is $2.22.

  6. Confidence Intervals for • 101.77 ( ) Definition: A c-confidence interval for the population mean is Find the 95% confidence interval for the one-way plane fare from Atlanta to Chicago. You found = 101.77 and E = 2.22 Right endpoint Left endpoint 103.99 99.55 With 95% confidence, you can say the mean one-way fare from Atlanta to Chicago is between $99.55 and $103.99.

  7. Sample Size Given a c-confidence level and an maximum error of estimate, E, the minimum sample size n, needed to estimate , the population mean is You want to estimate the mean one-way fare from Atlanta to Chicago. How many fares must be included in your sample if you want to be 95% confident that the sample mean is within $2 of the population mean? You should include at least 43 fares in your sample. Since you already have 35, you need 8 more.

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