Math 1025 - Lesson Plan Chapter 6v1

Math 1025 - Lesson Plan Chapter 6v1 - Chapter 6 Confidence...

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Chapter 6 - Confidence Intervals Section 6.1 - Confidence Intervals for the Mean (Large Samples) Objectives Find a point estimate and a margin of error Construct and interpret confidence intervals for the population mean Determine the minimum sample size required when estimating μ 1) Point Estimate - (a) A single value estimate for a population parameter (b) Most unbiased point estimate of the population mean μ is the sample mean . { Estimate μ with }. Try It Yourself 1 - (p. 310) Another random sample of number of sentences found in 30 magazine advertisements is listed {16 9 14 11 17 12/ 99 18 13 12 5 9 / 17 6 11 17 18 20 / 6 14 7 11 12 12 /5 11 18 6 4 13} Use this sample to find a point estimate for μ (different from example 1). a. Find the Sample Mean. b. Estimate the mean sentence length of the population. 2) Interval estimate - An interval, or range of values, used to estimate a population parameter. 3) Level of confidence c - The probability that the interval estimate contains the population parameter. Most used Confidence Levels, {where Z c (and -Z c ) are called Critical Values}: Level of Confidence 90% 1.645 95% 1.96 99% 2.575 4) Sampling error - The difference between the point estimate and the actual population parameter value. For μ: the sampling error is the difference μ is generally unknown varies from sample to sample 5) Margin of error - The greatest possible distance between the point estimate and the value of the parameter it is estimating for a given level of confidence, c . Denoted by , if n≥30 , the sample standard deviation can be used for σ . Try It Yourself 2 - (p. 312) Use the data in TIY #1 and a 95% confidence level to find the margin of error for the mean number of sentences ina magazine advertisement. # of sentences in magazine ads data = {16 9 14 11 17 12/ 99 18 13 12 5 9 / 17 6 11 17 18 20 / 6 14 7 11 12 12 /5 11 18 6 4 13} a. Identify z c , n and s. b. Find E using z c , σ ≈ s, and n. c. State the margin of error. 6) Confidence Intervals for the Population Mean → (the probability that the confidence interval contains μ is c.) Constructing Confidence Intervals for μ (Population Means) In Words In Symbols 1. Find the sample statistics n and .
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2. Specify σ , if known. Otherwise, if n 30, find the sample standard deviation s and use it as an estimate for . 3. Find the critical value z c that corresponds to the given level of confidence. Use the Standard Normal Table. 4. Find the margin of error E 5. Find the left and right endpoints and form the confidence interval. Left endpoint: Right endpoint: Interval: Try It Yourself 3 - (p. 314) Use the sample data in TIY #1 to construct 95% confidence intervals for the mean number of sentences in all magazine advertisements. Compare results with the interval found in example 3. # of sentences in magazine ads data = {16 9 14 11 17 12/ 99 18 13 12 5 9 / 17 6 11 17 18 20 / 6 14 7 11 12 12 /5 11 18 6 4 13} a. Find b. Find the left and right end points of the confidence interval.
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Math 1025 - Lesson Plan Chapter 6v1 - Chapter 6 Confidence...

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