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Unit 7 Section 6.1. 6.1: Confidence Intervals for the Mean (σ is known)  Estimation is a primary aspect of inferential statistics. It allows us to estimate.

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Presentation on theme: "Unit 7 Section 6.1. 6.1: Confidence Intervals for the Mean (σ is known)  Estimation is a primary aspect of inferential statistics. It allows us to estimate."— Presentation transcript:

1 Unit 7 Section 6.1

2 6.1: Confidence Intervals for the Mean (σ is known)  Estimation is a primary aspect of inferential statistics. It allows us to estimate the value of a parameter based on information collected from a sample.  For example: “The average kindergarten student has seen more than 5000 hours of television” “Four out of five doctors recommend …”  Since the populations for these values are large, the values are estimates of the parameters.

3  Point estimate – a specific numerical value estimate for a population parameter.  The best point estimate of the population mean is the sample mean.  This is because the sample mean varies less than other statistics.  Estimator – a statistic used to estimate a parameter. Section 6.1

4 Three Properties of a Good Estimator  The estimator should be an unbiased estimator.  The expected value (or the mean on the estimates) should be equal to the parameter being estimated.  The estimator should be consistent.  As sample size increases, the value of the estimator approaches the value of the parameter being estimated.  The estimator should be a relatively efficient estimator.  Of all the statistics that can be used to estimate a parameter, the relatively efficient estimator has the smallest variance. Section 6.1

5  Example 1: An economics researcher is collecting data about grocery store employees in a county. The data listed below represents a random sample of the number of hours worked by 40 employees from several grocery stores in the county. Find a point estimate of the population mean Section 6.1

6  Interval estimate – an interval or range of values used to estimate the parameter.  This may or may not contain the value of the parameter being estimated.  A degree of confidence (usually a percent) can be assigned before the estimation is made. The larger the percent, the larger the interval.  Level of Confidence – the probability that the interval estimate will contain the parameter.  This assumes that a large number of samples are selected and that the estimation process on the same parameter is repeated.  Confidence interval – estimate of a parameter determined by using data obtained from a sample and by using the specific confidence level of the estimate. Section 6.1

7  The three common confidence intervals used are: 90%, 95%, and 99%.  In the confidence interval formula, α(alpha) represents the total area of both tails of the standard normal distribution curve. Section 6.1

8  Margin of error E (a.k.a. maximum error of the estimate) – the greatest possible difference between the point estimate and the value of the parameter.  Notation: Must fulfill the following conditions:  The sample is random  The population is normally distributed OR n ≥ 30 When rounding a confidence interval, round to the same number of decimal places as the mean. Section 6.1

9  Example 2: Using the information from Example 1, determine the margin of error (E) for a confidence of 95% (z = 1.96). Assume the standard deviation for the population is 7.9 hours. Section 6.1

10 Formula for the Confidence Interval of the Mean for a Specificα  For a 90% confidence interval, use:  For a 95% confidence interval, use:  For a 99% confidence interval, use: Section 6.1

11  Example 3: Use the data from Examples 1 and 2 to construct a 95% confidence interval for the mean number of hours worked by the grocery store employees. Section 6.1

12 Homework:  Pg 305 : #’s 1 – 32  Read and Take Notes on Section 6.1 (pgs ) Section 6.1


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