Chapter 8b Confidence Intervals

# Chapter 8b Confidence Intervals - Click to edit Master...

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Unformatted text preview: Click to edit Master subtitle style © Professor Thomas R. Sexton © Professor Thomas R. Sexton 11 Confidence Intervals Professor Thomas R. Sexton College of Business Stony Brook University © Professor Thomas R. Sexton © Professor Thomas R. Sexton 22 Our First Estimation Problem n What proportion of Stony Brook students smoke? n Very large population ( N ≈ 23,000). n Sample size = n = 100 students n X = 20 students smoke © Professor Thomas R. Sexton © Professor Thomas R. Sexton 33 Constructing an Interval Estimate n What we want is an interval of the form: n This is an interval that has a predetermined probability of “capturing” π , the unknown population parameter. n How should we compute the endpoints? © Professor Thomas R. Sexton © Professor Thomas R. Sexton 44 Solve for π © Professor Thomas R. Sexton © Professor Thomas R. Sexton 55 Confidence Interval for π © Professor Thomas R. Sexton © Professor Thomas R. Sexton 66 What Proportion of Stony Brook Students Smoke? © Professor Thomas R. Sexton © Professor Thomas R. Sexton 77 Margin of Error (Sampling Error) n In any confidence interval, the part after the ± is called the margin of error or the sampling error . n Together with the confidence level, the margin of error tells us how precisely we have estimated the parameter. n In this example, we say that “we have a margin of error of 0.0784 (or 7.84 percentage points) with 95% confidence.” © Professor Thomas R. Sexton © Professor Thomas R. Sexton 88 Changing the Confidence Level © Professor Thomas R. Sexton © Professor Thomas R. Sexton 99 Finite Populations: Confidence Intervals n When our sample size, n , is more than 5% of the population, N , and we are sampling without replacement, then we need to apply the Finite Population Correction Factor (FPCF) when computing confidence intervals. © Professor Thomas R. Sexton © Professor Thomas R. Sexton 1010 Confidence Interval for with FPCF π © Professor Thomas R. Sexton © Professor Thomas R. Sexton 1111 What Proportion of Business Management Majors Smoke? © Professor Thomas R. Sexton © Professor Thomas R. Sexton 1212 Our Other Estimation Problem n How satisfied are your customers? n Very large population ( N = 10,000) n Random sample of n = 100 customers n You compute the mean and SD of the n = 100 customer satisfaction scores (on a scale of 0 – 100): © Professor Thomas R. Sexton © Professor Thomas R. Sexton 1313 Constructing an Interval Estimate n What we want is an interval of the form: n This is an interval that has a predetermined probability of “capturing” μ , the unknown population parameter. n How should we compute the endpoints? © Professor Thomas R....
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Chapter 8b Confidence Intervals - Click to edit Master...

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