We wish to compare the expected values, Hx and phy of two independent normal pop

Question

We wish to compare the expected values, Hx and phy of two independent normal populations, say X and Y, with known standard deviations = 1.1 and phy = 1.3. we take a random sample of size 12 from X (X1,X2, ... ,X12) and a random sample of size 9 from Y (Y1,Y2, ... ,Yg) as follows: 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, 5.61, 5.17, 6.93, 3.37, 6.06, 4.15, 5.83 We are interested in examining 4x - Hy. Call the sample means of X and Y, Xbar and Ybar respectively(xbar and ybar realized values). Assume that all distributions are normal. Use R for computations. a)Calculate xbar || b) Calculate the variance of Xbar c) Calculate ybar| d) Calculate the variance of Ybar. e) Calculate the variance of Xbar - Ybar. f) What is the critical value used for a 95% confidence interval for Ax - hy? 9) Create a 95% confidence interval for dx - ly. ( , 1) What is the length of your 95% confidence interval for pux - hy? 3) What would the p value have been if we used this data to test Houx - Hy=0 against the alternative Ha:Ax - Hy > 0?

Explanation / Answer

a) x = c(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 = c(5.34,6.43,5.61,5.17,6.93,3.37,6.06,4.15,5.83)
> x_bar = mean(x)
> x_bar
[1] 5.144167

b) Var_xbar = var(x)
> Var_xbar
[1] 1.448481

c) y_bar=mean(y)
> y_bar
[1] 5.432222

d)  var_ybar=var(y)
> var_ybar
[1] 1.224619

e) Var_xbar-var_ybar
[1] 0.2238616
>

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