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Chapter 09 - Sections 1, 2 &amp; Chapter 07 - Section 4

# Chapter 09 - Sections 1, 2 &amp; Chapter 07 - Section 4...

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Chapter 9 Estimating the Value of a Parameter Using Confidence Intervals Fall 2008 1

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Chapter 9 Section 1 The Logic in Constructing Confidence Intervals about a Population Mean where the Population Standard Deviation is Known Fall 2008 2
Confidence Intervals Learning objectives Compute a point estimate of the population mean Construct and interpret a confidence interval about the population mean (assuming the population standard deviation is known) Understand the role of margin of error in constructing a confidence interval Determine the sample size necessary for estimating the population mean within a specified margin of error Fall 2008 3

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Confidence Intervals We apply the results about the sample mean to the problem of estimation Estimation is the process of using sample data to estimate the value of a population parameter We will quantify the accuracy of our estimation process Fall 2008 4
Confidence Intervals Estimation involves two steps Step 1 – to obtain the value of a statistic that estimates the value of a parameter, this is called the point estimate Step 2 – to quantify the accuracy and precision of the point estimate The first step is relatively easy The second step is why we need statistics Fall 2008 5

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Confidence Intervals Some examples of point estimates are: The sample mean to estimate the population mean The sample standard deviation to estimate the population standard deviation The sample proportion to estimate the population proportion The sample median to estimate the population median Fall 2008 6
Confidence Intervals Our goal in this section is to estimate the value of an unknown population mean A point estimate of a parameter is a single value of some statistic A confidence interval estimate consists of an interval of values determined from sample information. Associated with the interval is a percentage that measures one’s confidence that the parameter lies within the interval Fall 2008 7

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Confidence Intervals The amount of confidence associated with an interval is called the confidence level, and this may be expressed as a percentage or a decimal. Although the choice of the confidence level is at the discretion of the experimenter, the most commonly used values are 90 percent, 95 percent, and 99 percent. Fall 2008 8
Confidence Intervals What does the level of confidence represent? If we have a process for calculating confidence intervals with a 90% level of confidence Assume that we know the population mean We then obtain a series of 50 random samples We apply our process to the data from each random sample to obtain a confidence interval for each Then, we would expect that approximately 90% of those 50 confidence intervals (or about 45) would contain our population mean Helpful Hint: Look over Example 2 on pp. 407-410 of your textbook Fall 2008 9

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Confidence Intervals The level of confidence is always expressed as a percent
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Chapter 09 - Sections 1, 2 &amp; Chapter 07 - Section 4...

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