chap08 - Statistics for Business and Economics Chapter 8...

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Chap 8-1 Chapter 8 Estimation: Additional Topics Statistics for Business and Economics
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Chap 8-2 Chapter Goals After completing this chapter, you should be able to: Form confidence intervals for the mean difference from dependent samples Form confidence intervals for the difference between two independent population means ( standard deviations known or unknown) Compute confidence interval limits for the difference between two independent population proportions Create confidence intervals for a population variance Find chi-square values from the chi-square distribution table Determine the required sample size to estimate a mean or proportion within a specified margin of error
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Chap 8-3 Estimation: Additional Topics Chapter Topics Population Means, Independent Samples Population Means, Dependent Samples Population Variance Group 1 vs. independent Group 2 Same group before vs. after treatment Variance of a normal distribution Examples: Population Proportions Proportion 1 vs. Proportion 2
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Chap 8-4 Dependent Samples Tests Means of 2 Related Populations Paired or matched samples Repeated measures (before/after) Use difference between paired values: Eliminates Variation Among Subjects Assumptions: Both Populations Are Normally Distributed Dependent samples d i = x i - y i
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Chap 8-5 Mean Difference The i th paired difference is d i , where d i = x i - y i The point estimate for the population mean paired difference is d : n d d n 1 i i = = n is the number of matched pairs in the sample 1 n ) d (d S n 1 i 2 i d - - = = The sample standard deviation is: Dependent samples
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Chap 8-6 Confidence Interval for Mean Difference The confidence interval for difference between population means, μ d , is Where n = the sample size (number of matched pairs in the paired sample) n S t d μ n S t d d α/2 1, n d d α/2 1, n - - + < < - Dependent samples
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Chap 8-7 The margin of error is t n-1, α /2 is the value from the Student’s t distribution with (n – 1) degrees of freedom for which Confidence Interval for Mean Difference (continued) 2 α ) t P(t α/2 1, n 1 n = - - n s t ME d α/2 1, n - = Dependent samples
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Chap 8-8 Six people sign up for a weight loss program. You collect the following data: Paired Samples Example Weight : Person Before (x) After (y) Difference, d i 1 136 125 11 2 205 195 10 3 157 150 7 4 138 140 - 2 5 175 165 10 6 166 160 6 42 d = Σ d i n 4.82 1 n ) d (d S 2 i d = - - = = 7.0
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Chap 8-9 For a 95% confidence level, the appropriate t value is t n-1, α /2 = t 5,.025 = 2.571 The 95% confidence interval for the difference between means, μ d , is 12.06 μ 1.94 6 4.82 (2.571) 7 μ 6 4.82 (2.571) 7 n S t d μ n S t d d d d α/2 1, n d d α/2 1, n < < - + < < - + < < - - - Paired Samples Example (continued) Since this interval contains zero, we cannot be 95% confident, given this limited data, that the weight loss program helps people lose weight
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Chap 8-10 Difference Between Two Means Population means,
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This note was uploaded on 11/16/2011 for the course ECON 101 taught by Professor Peter during the Spring '11 term at FH Wiener Neustadt.

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chap08 - Statistics for Business and Economics Chapter 8...

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