1. A reasher wanted to determine if the average size of farmsin two countries in
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1. A reasher wanted to determine if the average size of farmsin two countries in Pennsylvania were different. He samples 8 farmsin Indiana County and determines the average size of a farm is 191acres with a standard deviation of 38 acres. He then samples 10farms in Greene County and determines the average size of a farm is199 acres with a standard deviation of 12 acres. A hypothesis testwas conducted at the 5 % level of significance. A. Accept the alternative hypothesis B. Reject the null hypothesis C. Do not reject the null hypothesis D. Do not reject the alternative hypothesis E. Reject the alternative hypothesis. 2. A researcher wanted to determine if the average size offarms in two counties in Pennsylvania were different. He samples 8farms in Indiana County and determine the average size of a farm is191 acres with a standard deviatiom of 38 acres. He then samples 10farms in Green County and determines the average size of a farm is199 acres with a standard deviation of 12 acres. A. (24,11, 40.11) B. (18.52, 56.24) C. (-40.11, 24.11) D. (-34.85, 18.846) E. (-18.846, 34.85) 1. A reasher wanted to determine if the average size of farmsin two countries in Pennsylvania were different. He samples 8 farmsin Indiana County and determines the average size of a farm is 191acres with a standard deviation of 38 acres. He then samples 10farms in Greene County and determines the average size of a farm is199 acres with a standard deviation of 12 acres. A hypothesis testwas conducted at the 5 % level of significance. A. Accept the alternative hypothesis B. Reject the null hypothesis C. Do not reject the null hypothesis D. Do not reject the alternative hypothesis E. Reject the alternative hypothesis. 2. A researcher wanted to determine if the average size offarms in two counties in Pennsylvania were different. He samples 8farms in Indiana County and determine the average size of a farm is191 acres with a standard deviatiom of 38 acres. He then samples 10farms in Green County and determines the average size of a farm is199 acres with a standard deviation of 12 acres. A. (24,11, 40.11) B. (18.52, 56.24) C. (-40.11, 24.11) D. (-34.85, 18.846) E. (-18.846, 34.85)Explanation / Answer
n1=8, xbar1=191, s1=38 n2=10, xbar2=199, s2=12 =0.05, t(0.025, df=n1+n2-2=8+10-2=16)=-2.12 1. The test hypothesis is Ho:1-2=0 Ha:1-2 not equal 0 The test statistic is t=(xbar1- xbar2)/ sqrt(s1^2/n1 + s2^2/ n2) =(191-199)/ sqrt(38^2/8 + 12^2/10) =-0.57 Since t=-0.57> -2.12, do not reject Ho. ------------------------------------------------------------------------------------- 2. The 95% CI is (xbar1- xbar2)±t*sqrt(s1^2/n1 + s2^2/ n2) -->(191-199)±2.12*sqrt(38^2/8 + 12^2/10) -->(-37.6, 21.6)
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