We wish to compare the expected values, μx
and μy of two independent normal populations,
say X and Y, with known standard deviations μx
= 1.1 and μy = 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, …
,Y9
) 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 μx –
μy. Call the sample means of X and Y, Xbar and
Ybar respectively(xbar and ybar realized values). Assume that all
distributions are normal. SHOW R WORK
c) Calculate the variance of Xbar
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 μx –
μy?
g) Create a 95% confidence interval for μx –
μy.
i) What is the length of your 95% confidence interval for
μx – μy?
j) What would the p value have been if we used this data to test
H0:μx –
μy=0
against the alternative Ha:μx –
μy > 0
?
