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# ECO202 formulae

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Formulas compiled for Statistics for economics

For Mr. Iftekharul Haque's class

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### ECO202 formulae

1. 1. CHAPTER 7 Sampling Distribution of Sample Mean  Population distribution μ X N i  18  20  22  24  21 σ  4  (X i  μ)2 N  2.236  N= Population size n= sample size  Sample mean X  1 n  Xi n i 1  Standard Error of mean σ X  μX  μ  Normal distribution  σ (standard error of the mean decreases as the sample size increases) n σX  X = sample mean μ = population mean σ n σ = population standard deviation Z Then, Z-value for the sampling distribution of X n = sample size (X  μ) (X  μ)  σ σX n  Finite population correction----n > 5% of N σ2 N  n n N 1 σX  σ n Nn N 1  Then, Var( X)   If the n is not small compared to the N , then use Z   Sampling distribution property---- as n increases, (X  μ) σ Nn n N 1 σ x decreases Central Limit Theorem: As n increases Sampling Distribution becomes normal. For n>25 Central Tendency μ X  μ Variation σ X  σ n  the interval - zα/2 to zα/2 encloses probability 1 – α Then μ  z/2σ X is the interval that includes X with probability 1 – α
2. 2. 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 PP  σP ˆ ˆ PP 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
3. 3.  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
4. 4.  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