297 Where You’re Going In this chapter, you will begin your study of inferential statistics—the second major branch of statistics. For instance, a chess club wants to estimate the mean IQ of its members. The mean of a random sample of members is 115. Because this estimate consists of a single number represented by a point on a number line, it is called a point estimate. The problem with using a point estimate is that it is rarely equal to the exact parameter (mean, standard deviation, or proportion) of the population. In this chapter, you will learn how to make a more meaningful estimate by specifying an interval of values on a number line, together with a statement of how confident you are that your interval contains the population parameter. Suppose the club wants to be 90% confident of its estimate for the mean IQ of its members. Here is an overview of how to construct an interval estimate. Where You’ve Been In Chapters 1 through 5, you studied descriptive statistics (how to collect and describe data) and probability (how to find probabilities and analyze discrete and continuous probability distributions). For instance, psychologists use descriptive statistics to analyze the data collected during experiments and tests. One of the most commonly administered psychological tests is the Wechsler Adult Intelligence Scale. It is an intelligence quotient (IQ) test that is standardized to have a normal distribution with a mean of 100 and a standard deviation of 15. 119 114 115 116 117 118 113 112 111 115 3.3 3.3 x 111.7 118.3 Find the mean of a random sample. x = 115 Find the margin of error. E = 3.3 Find the interval endpoints. Left: 115 − 3.3 = 111.7 Right: 115 + 3.3 = 118.3 Form the interval estimate. 111.7 < < 118.3 μ So, the club can be 90% confident that the mean IQ of its members is between 111.7 and 118.3.
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