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5169e59a-2703-43ae-acf0-e03bcb5eacd3

5169e59a-2703-43ae-acf0-e03bcb5eacd3 - Chapter 8 Confidence...

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Chapter 8 Chapter 8 Confidence Intervals Aims In this chapter we deal with: Constructing confidence intervals by hand The level of confidence The width of the confidence interval Sample size issues The margin of error Interpreting confidence intervals By the end of this chapter you should: be able to state the 4 parameters that we build confidence intervals for in this chapter know how to construct a confidence interval by hand for each of these 4 parameters be able to interpret a confidence interval in plain English understand the nature of confidence levels what is meant by the level of confidence what affects the width of a confidence interval what is meant by the margin of error Page 1 Single Mean, μ Part Time Work I What is the average number of hours worked per week by all those Stage 1 Statistics students who have a part time job through the semester? Hours worked per week: 25 12 10 20 13 12 13 4 8 6 15 12 (12 students) (Source: Stage 1 Statistics online survey ) Method: Use the sample data, to produce a range of believable values for μ , i.e., an interval estimate. Assume the 12 observations form a random sample from a population with mean μ . Use the sample mean, x = 12.5 hours as a (point) estimate for μ . This estimate is based upon a particular sample; another sample with 12 different students would give a different value for the estimate, i.e., this estimate value varies from sample to sample. We say ‘this estimate is subject to sampling variability’. Place a t-standard-error interval around the estimate to allow for the uncertainty due to the sampling variability: estimate ± t × se( estimate ) Set this method’s success rate at 95% (i.e., very likely to work) Assume the data come from a Normal distribution, i.e,, the population has a Normal distribution Use the Student’s t -distribution to determine how many standard errors (the t -multiplier’) to use in constructing the interval. Summary statistics: x = 12.5 hours s = 5.73 hours n = 12 Population (Stage 1 Statistics students who have part time work) Sample (12 students) X = hours worked μ X ? (parameter) x (estimate)
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