Point Estimates and Confidence Intervals

# Point Estimates and Confidence Intervals - sample of...

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Point Estimates and Confidence Intervals You have seen that the sample mean  is an unbiased estimate of the population mean μ. Another  way to say this is that  is the best point estimate of the true value of μ. Some error is associated with  this estimate, however—the true population mean may be larger or smaller than the sample mean.  Instead of a point estimate, you might want to identify a range of possible values  p  might take,  controlling the probability that μ is not lower than the lowest value in this range and not higher than  the highest value. Such a range is called a  confidence interval Example 1 Suppose that you want to find out the average weight of all players on the football team at Landers  College. You are able to select ten players at random and weigh them. The mean weight of the
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Unformatted text preview: sample of players is 198, so that number is your point estimate. Assume that the population standard deviation is = 11.50. What is a 90 percent confidence interval for the population weight, if you σ presume the players' weights are normally distributed? This question is the same as asking what weight values correspond to the upper and lower limits of an area of 90 percent in the center of the distribution. You can define that area by looking up in Table 2 (in "Statistics Tables") the z-scores that correspond to probabilities of 0.05 in either end of the distribution. They are −1.65 and 1.65. You can determine the weights that correspond to these z-scores using the following formula:...
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