00027 000192 000303 000481 000538 000583 000649

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Unformatted text preview: 514 0.66237 0.00234 0.71205 0.18037 0.71607 0.90512 Note: Rows 10­901 are not shown. ECO 3411 23 Using Excel to Select a Simple Random Sample • Value Worksheet (Sorted) A 1 2 3 4 5 6 7 8 9 B C D Applicant Number 12 773 408 58 116 185 510 394 SAT Score 1107 1043 991 1008 1127 982 1163 1008 On-Campus Housing No Yes Yes No Yes Yes Yes No Random Number 0.00027 0.00192 0.00303 0.00481 0.00538 0.00583 0.00649 0.00667 Note: Rows 10­901 are not shown. ECO 3411 24 Example: UCF • Point Estimates – x as Point Estimator of µ ∑x x= 29,910 = = 997 30 30 i – s as Point Estimator of σ s= ( xi − x )2 ∑ 29 = 163,996 = 75.2 29 – p as Point Estimator of p p = 20 30 = .68 • Note: Different random numbers would have identified a different sample which would have resulted in different point estimates. ECO 3411 25 Summary of Point Estimates Obtained from a Simple Random Sample Population Parameter Parameter Value Point Estimator Point Estimate µ = Population mean SAT score 990 x = Sample mean 997 σ = Population std. deviation for SAT score 80 s = Sample std. deviation for SAT score 75.2 p = Population pro­ portion wanting campus housing .72 SAT score p = Sample pro­ portion wanting campus housing ECO 3411 .68 26 Sampling Distribution of x • Process of Statistical Inference Population A simple random sample of n elements is selected from the population. with mean µ = ? x The value of is used to make inferences about the value of µ. ECO 3411 The sample data provide a value for x the sample mean . 27 Sampling Distribution of x • The sampling distribution of x is the probability distribution of all possible values of the sample mean x . • Expected Value of x E( x ) = µ where: µ = the population mean For this class ALWAYS INFINITE ECO 3411 28 Sampling Distribution of s Standard Deviation of x x FOR THIS CLASS ALWAYS INFINITE POPULATION σ σx = n • is referred to as the standard error of the mean. ECO 3411 29 Example • Let us assume a population of N=5 • We can have 5 possible sample of size 4(order is not important). X A 1 B 2 C 3 D 4 E 5 Pop Mean 3 ECO 3411 30 Continued A 1 B 2 C 3 D 4 Sample mean1 A B D E Sample mean 4 2.5 B C D E Sample mean 2 2 3 4 5 3.5 A C D E Sample mean 3...
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This note was uploaded on 01/17/2014 for the course ECO 3411 taught by Professor Staff during the Winter '08 term at University of Central Florida.

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