Q1. Ans Pooled variance t test is Answer Value of Combined Standard deviation is S= (n1*s1^2 + n2*s2^2 )/(n1+n2-2) we use Test Statistic (t) = (X-Y)/Sqrt(S^2(1/n1+1/n2)) Q2. Ans Confidence Interval CI = x ? Z a/2 * (sd/ Sqrt(n)) Where, x = Mean sd = Standard Deviation a = 1 - (Confidence Level/100) Za/2 = Z-table value CI = Confidence Interval Mean(x)=42144 Standard deviation( sd )=3000 Sample Size(n)=10 Confidence Interval = [ 42144 ? Z a/2 ( 3000/ Sqrt ( 10) ) ] = [ 42144 - 1.96 * (948.6833) , 42144 + 1.96 * (948.6833) ] = [ 40284.5807,44003.4193 ] None of the above is Answer Q3. Ans x = Mean n = Sample Size a = 1 - (Confidence Level/100) Za/2 = Z-table value CI = Confidence Interval Mean(x)=54.4 Sample Size(n)=80 Sample proportion = x/n =0.68 Confidence Interval = [ 0.68 ?Z a/2 ( Sqrt ( 0.68*0.32) /80) ] = [ 0.68 - 1.96* Sqrt(0.0027) , 0.68 + 1.96* Sqrt(0.0027) ] = [ 0.578,0.782] ~ [ 57.8% , 78.2% ] 58; 78 is Answer Q4. CI = x ? Z a/2 * (sd/ Sqrt(n)) Where, x = Mean sd = Standard Deviation a = 1 - (Confidence Level/100) Za/2 = Z-table value CI = Confidence Interval Mean(x)=15.23 Standard deviation( sd )=1.65 Sample Size(n)=24379 Confidence Interval = [ 15.23 ? Z a/2 ( 1.65/ Sqrt ( 24379) ) ] = [ 15.23 - 1.96 * (0.0106) , 15.23 + 1.96 * (0.0106) ] = [ 15.2093,15.2507 ] 15.21 ; 15.25 is Answer Q5. Under The Null Hypothesis H0:P=0.77 Under The Alternate Hypothesis H ...
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