Question

The following values were measured from an instrument B 65 A 87 80 83 77 90 91 82 90 66 73 84 80 Mean(A)=83.5 Std(A)=4.6797 n=6 f=5 Mean(B)=78.14 Std(B)=10.57 n=7 f=6 Are the instruments equal? Calculate a confidence interval for the difference between the instruments and construct a hypothesis to perform the appropriate statistical test.

Answer 1

given - * = $3.5 72 = 78.14 X2 = 78.14,- 6 = 4.6797 Sy = 10:57 ny7 To tist Hoi 1 =12 Vs H, : 4 & 42 Assuming population Van'aneer are equal Test statistics - t X - X, (n-1)32+ (9-0) 52 (tha) 7:) 83.5, -78.14 (6-1) (4.6797)2+(2-0) 10:57)? 6+7 - 2 U t 1:144 at K=0.05 , dife II we get critical value as, tc = 2.201 decision - Here It: 1.144 to = 3.201 so we accept Hot also p-value = 0,2768 7,0.05 conclusion we have sufficient evidence to conclude that instruments means are equal. Now, 957. Confidence interval for el-, is [x = tcx (n-1)5?+ (120) $} {** ) ni+n₂-2 2.2014 S x(4.67902 + 6X(10:57) 6+ 7-2 89.5-78.15 F

= (-4.95, 15.67) -4.95<u, a M2 < 15.67 is required 95% confidence interval for u, a42

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