chap06S4PRN

# A random sample of n 9 tax filers is taken econ 325

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A random sample of n = 9 tax filers is taken. Econ 325 – Chapter 6.4 6 Find a value a such that: 0.05 = < ) a s ( P X This is equivalent to finding a value a such that: 0.05 = < ) a s ( P 2 2 X The probability can be stated: 0.05 (30)(30) 8 = < χ = σ - < σ - = < 2 2 2 2 ) 8 ( 2 2 X 2 2 X a P a ) 1 n ( s ) 1 n ( P ) a s ( P From the chi-square distribution table: ( ) 0.05 2.73 = < χ 2 ) 8 ( P Therefore, 2.73 (30)(30) 8 = 2 a Solving gives: 17.52 8 2.73 30 = = a That is, the probability is 0.05 that the sample standard deviation of time taken to complete the tax form is less than 17.52 minutes.

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Econ 325 – Chapter 6.4 7 The graph below illustrates ( ) 0.05 2.73 = < χ 2 ) 8 ( P PDF of 2 ) 8 ( χ 2.73 0 Area = 0.05 Area = 0.95 2 χ (chi-square) distribution critical values can be obtained with Microsoft Excel with the function: CHISQ.INV.RT (right-tail probability, degrees_of_freedom) or (the old version) CHIINV(right-tail probability, degrees_of_freedom) For the above example the critical value is found with CHISQ.INV.RT(0.95, 8) = 2.7326
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