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Information about ECO202 formulae

Formulas compiled for Statistics for economics

For Mr. Iftekharul Haque's class

For Mr. Iftekharul Haque's class

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Sampling Distribution of Sample Proportion: P= population proportion ˆ X ˆ P = sample proportion P n ˆ 0≤ P≤1 ˆ P has a binomial distribution, but can be approximated by a normal distribution when nP(1 – P) > 9 ˆ E( P) p Z X P(1 P) σ 2 Var ˆ P n n ˆ PP σP ˆ ˆ PP P(1 P) n Chapter 8 If P(a < < b) = 1 - (1 - ) is called the confidence level then the interval from a to b is called a 100(1 - )% confidence interval of . Confidence Intervals for σ2 Known: z table Point Estimate ± (Reliability Factor)(Standard Error) x z α/2 σ n Where margin of error= ME z α/2 σ n W= 2ME The margin of error can be reduced if the population standard deviation can be reduced (σ↓) The sample size is increased (n↑) The confidence level is decreased, (1 – ) ↓ Confidence Intervals for σ2 Unknown: t table x μ x =mean, s=standard deviation s/ n t degrees of freedom= v= n-1 P(t n 1 t n 1,α/2 ) α/2

x t n -1,α/2 S S μ x t n -1,α/2 n n where tn-1,α/2 is the critical value Confidence Intervals for the Population Proportion, p: P(1 P) n σP ˆ p z α/2 ˆ ˆ ˆ ˆ p(1 p) p(1 p) ˆ P p z α/2 n n Chapter 10 Key: Outcome (Probability) The power of a test is the probability of rejecting a null hypothesis that is false Power = P(Reject H0 | H1 is true) Power of the test increases as the sample size increases If Calculated z < Critical zα = Do not reject Ho If Calculated z > Critical zα = Reject Ho

p-Value Approach to Testing Smallest value of for which H0 can be rejected For two-tail Tests of the Population Proportion: σp ˆ P(1 P) n

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