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EX 31 - STAT 400 Examples for Spring 2011 1 Alex buys a...

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STAT 400 Examples for 04/27/2011 Spring 2011 1. Alex buys a package of Sour Jelly Beans. On the package, it says that 50% of all jelly beans are lemon, 30% are cherry, and 20% are lime. When Alex opens the package, he finds 15 lemon, 9 cherry and 12 lime jelly beans. Is there enough evidence to conclude that the true proportions are different from the ones listed on the package? Use α = 0.05. a) State H 0 and H 1 . H 0 : p 1 = 0.50, p 2 = 0.30, p 3 = 0.20. H 1 : not H 0 . b) Find the expected frequencies under H 0 . n = 15 + 9 + 12 = 36 . E 1 = n p 10 = 36 × 0.50 = 18 . E 2 = n p 20 = 36 × 0.30 = 10.8 . E 3 = n p 30 = 36 × 0.20 = 7.2 . c) Calculate the values of the Q test statistic. 1 2 3 Total O 15 9 12 36 E 18 10.8 7.2 36 ( ) E E O 2 - ( ) 18 18 15 2 - ( ) 10.8 8 . 10 9 2 - ( ) 7.2 2 . 7 12 2 - 0.5 0.3 3.2 4.0 d) Find the critical value 2 α χ . 3 – 1 = 2 degrees of freedom. 2 05 . 0 χ ( 2 ) = 5.991 . e) State your decision ( Accept H 0 or Reject H 0 ) at α = 0.05. Q 2 = 4.0 < 5.991 = 2 α χ . Do Not Reject H 0 .
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2. The financial manager in charge of accounts receivable department is concerned about the current economic slowdown, because customers sometimes wait longer to pay their bills.
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