Chapter 9 Lesson 9.1 Estimation Using a Simple Sample 9.1: Point Estimation.

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Presentation transcript:

Chapter 9 Lesson 9.1 Estimation Using a Simple Sample 9.1: Point Estimation

Point Estimate A single number (a statistic) based on sample data that is used to estimate a population parameter It is not always equal to the population characteristic due to sampling variation “point” refers to the single value on a number line. Different samples may produce different statistics. Population characteristic

The paper reports the results of 7421 students at 40 colleges and universities. The authors want to estimate the proportion (p) of college students who spend more than 3 hours a day on the Internet out of 7421 students reported using the Internet more than 3 hours a day. This is a point estimate for the population proportion of college students who spend more than 3 hours a day on the Internet. p = 2998/7421 =.404

The paper “The Impact of Internet and Television Use on the Reading Habits and Practices of College Students” (Journal of Adolescence and Adult Literacy, 2009) investigates the reading habits of college students. The following observations represent the number of hours spent on academic reading in 1 week by 20 college students If a point estimate of , the mean academic reading time per week for all college students, is desired, an obvious choice of a statistic for estimating  is the sample mean x. However, there are other possibilities – a trimmed mean or the sample median.

College Reading Continued The mean of the middle 16 observations. So which of these point estimates should we use?

Choosing a Statistic for Computing an Estimate Choose a statistic that is unbiased (accurate) A statistic whose mean value is equal to the value of the population characteristic being estimated is said to be an unbiased statistic. Unbiased, since the distribution is centered at the true value Biased, since the distribution is NOT centered at the true value

Choosing a Statistic for Computing an Estimate Choose a statistic that is unbiased (accurate) Choose a statistic with the smallest standard deviation Unbiased, but has a larger standard deviation so it is not as precise. Unbiased, but has a smaller standard deviation so it is more precise. If the population distribution is normal, then x has a smaller standard deviation than any other unbiased statistic for estimating .

If there’s time…YouTube AP Stats Guy - "WHAT IS A CONFIDENCE INTERVAL???”AP Stats Guy - "WHAT IS A CONFIDENCE INTERVAL???”

Homework Pg.441: #9.3, 4 (ignore the biased part in c)