010+Correlation

If we have a large sample n 30 the 1 condence interval

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Unformatted text preview: freedom df = n − 2. If H0 is not rejected we may conclude (only in the normal case) that random variables X and Y are independent with the probability P = 1 − α. Condence interval for a correlation coecient. Assume that X and Y are normally distributed. If we have a large sample (n ≥ 30) the (1 − α)% condence interval for a correlation coecient is 1 − ρ2 ˆ ρ ± zα/2 √ ˆ n 5 A. Zhensykbaev Correlation i.e. 1 − ρ2 ˆ 1 − ρ2 ˆ ρ − zα/2 √ , ρ + zα/2 √ ˆ ˆ . n n We want to estimate ρ to within a given boundary for sampling error SE. How much will be the sample size n to accomplish this? (zα/2 (1 − ρ2 ))2 ˆ n= . (SE )2 Example 1. Consider the monthly sales revenue as a function of the monthly advertising expenditure. We base on the following table and test the hypothesis: sales revenue and advertising expenditure are independent (use α = 0.02). Advertising Sales Month expenditure Revenue xi ($100) yi ($1000) 1 1 1 2 2 1 3 3 2 4 4 2 5 5 4 Total xi = 15 yi = 10...
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