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

Question

We wish to compare the expected values, ex and phy of two independent normal populations, say X and Y, with known standard deviations plx = 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 norma Use R for computations. a)Calculate xbar 5.1442 b) Calculate the variance of Xbar 0.1008 c) Calculate ybar 5.4322 d) Calculate the variance of Ybar. 0.1877 e) Calculate the variance of Xbar - Ybar. 0.2886 f) What is the critical value used for a 95% confidence interval for Ax - Hy? 1.9599 9) Create a 95% confidence interval for fx - Hy: ( -1.3409 - , 0.7648 I) What is the length of your 95% confidence interval for Ax - Hy? 2.1058 3) What would the p value have been if we used this data to test Ho:ux - Ay=0 against the alternative Ha:4x - Hy > 0 ? 0.9100394

Explanation / Answer

calcualtion t-statistics

Difference Scores Calculations

Treatment 1

N1: 12
df1 = N - 1 = 12 - 1 = 11
M1: 5.14
SS1: 15.93
s21 = SS1/(N - 1) = 15.93/(12-1) = 1.45


Treatment 2

N2: 9
df2 = N - 1 = 9 - 1 = 8
M2: 5.43
SS2: 9.8
s22 = SS2/(N - 1) = 9.8/(9-1) = 1.22


T-value Calculation

s2p = ((df1/(df1 + df2)) * s21) + ((df2/(df2 + df2)) * s22) = ((11/19) * 1.45) + ((8/19) * 1.22) = 1.35

s2M1 = s2p/N1 = 1.35/12 = 0.11
s2M2 = s2p/N2 = 1.35/9 = 0.15

t = (M1 - M2)/(s2M1 + s2M2) = -0.29/0.26 = -0.56

The t-value is -0.56135. The p-value is .29056.

thanks

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