EX 30 - STAT 400 Examples for 11/17/2011 Fall 2011 1. A new...

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Examples for 11/17/2011 Fall 2011 1. A new method of storing snap beans is believed to retain more ascorbic acid than the old method. In an experiment, snap beans were harvested under uniform conditions and frozen in 250 equal-size packages. One hundred of those packages were randomly selected and stored according to the new method, and the other 150 packages were stored by the old method. Subsequently, ascorbic acid determinations (in mg/kg) were made, and the following summary statistics were calculated. New Method Old Method (sample) mean ascorbic acid 450 410 (sample) standard deviation 20 45 a) Construct a 95% confidence interval for the difference in the mean amount of ascorbic acid retained. n 1 = 100 and n 2 = 150 are large, t α / 2 can be approximated by z α / 2 . ( ) 2 2 2 1 2 1 2 α Y X n s n s z + ± - ( ) 150 45 100 20 96 . 1 410 450 2 2 + ± - 40 ± 8.2 ( 31.8 , 48.2 ) b) Perform the appropriate test at a 1% level of significance. Claim: μ New > μ Old H 0 : μ New μ Old = 0 vs. H 1 : μ New μ Old > 0 Test Statistic: Z = ( ) ( ) 150 45 100 20 0 410 450 Y X 2 2 2 2 2 1 2 1 0 s s δ + - - = + - - n n = 9.562. n
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EX 30 - STAT 400 Examples for 11/17/2011 Fall 2011 1. A new...

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