arst poires we wish to compare the expected values,and , or two independent norm

Question

arst poires we wish to compare the expected values,and , or two independent normal popolatons, say X and Y, with kneen x,.xz. Au } and a random sample of tize 9 fro n Y ( Y.r %) as follows: standard deviations .-1.1and»,-1.3 . we take a random sample of sur 12 from x( x: 3.84, 6.18, 5.85,5.82,3.66, 3.83,4.09,7.25, 5.69, 3.99,6.17,5.36 Y: 5.34, 6.43, s.61·5.17,6.93, 137, 606, 4.15, sa We are interested i, examining .·. Call the sample means of x end Xbar and Yber respectively(x ). Assume that all distributions ane normal. Use R for computations a)Cakculate xbar $144167 b)Calculate the variance of Xbar 0.13085 c) Calculate ytar 5432222 )Calculate the variance of Yba 0.753 e) Calculate tho variance of Xbar-Ybst O 206 r) what is the crtical vsve used for agg%, condence intervzi for '»,? create a 95% corfdence inerval for a,-ur ( -13029 What is the length of your 95% oondence iterval for-',? what would the p veloe heve been if we used this data to test H against the alternative "-:Pr-», > 0, a, .»,-

Explanation / Answer

a)xbar = 5.1275

b) var(Xbar) = 1.444

c)ybar = 5.4322

d)var(ybar) = 1.2246

e)

Var(xbar - ybar) = (0.5064)^2 = 0.2564

f) g) i) j)

Critical value = 1.7341

CI = (-1.1828 , 0.5733)

Length = 1.7561

j)

p-value = 0.2774

x1(bar) 5.13 x2(bar) 5.43 s1 1.20 s2 1.11 n1 12 n2 9 SE = sqrt[ (s12/n1) + (s22/n2) ] (s12/n1) 0.1203 (s22/n2) 0.1361 SE 0.5064

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