9.3 . we take a random sample of sue 11 we wish to co pare the expected values,
ID: 2946966 • Letter: 9
Question
9.3 . we take a random sample of sue 11 we wish to co pare the expected values, x and ?, of two independent non al populations, say x and Y, with known standard deviations ox-7.1 and av from x (x1,x2. x1 1 ) and a random sample of size 9 from ? (Y1h. …,Yo ) as folows: x: 19.22, 9.17,-1.84,12.26, 7.01, 17.61,-4.90, 11.90, 9.48, 15.44, 10.97 Y: 8.35, 20.98, 4.55, 14.72, 1.08, 13.10, -6.48, 5.03, 22.85 we are interested in examining a ?. Call the sample means of X and Y, Xer and Ybar respectively xbar and ybar reanzed values . Assume that all ast tutions are normal use R for computations a)Calculate xbar b) calculate the variance of Xbar c) Caloulate ybar d) Calculate the varlance of Ybar e) Calculate the variance of Xbar Ybar nwhat is the crescal value used for a 99% condence interval for ?'My? g) Create a 99% confidence interval for Pa-Pv. h)What is the length of your 99% condence interval for ?'?? o what would the p value have been it we used this data to test Ho:W-Py against the anernative naw" > 0?Explanation / Answer
(a)x-bar=mean=9.665454
(b) var(x-bar)=variance/n=4.5827
(c) y-bar=mean of y=8.342222
(d) var(y-bar)=variance/n=9.61
(e) var(x-bar - y-bar)=4.5827+9.61=14.1927
(f) critical value for 99% is 2.58
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