Question

Suppose you want to test the claim the the paired sample data given below come from a population for which the mean difference is μd=0μd=0.

x: 51 66 54 78 89 71 70  

y: 91 63 56 79 59 77 56

Use a 0.050.05 significance level to find the following:
(a)    The mean value of the differnces dd for the paired sample data
d⎯⎯⎯=d¯=
(b)    The standard deviation of the differences dd for the paired sample data
sd=sd=
(c)    The t test statistic
t=t=
(d)    The positive critical value
t=t=
(e)    The negative critical value
t=t=
(f)    Does the test statistic fall in the critical region?

A. Yes
B. No

(g)    Construct a 9595% conficence interval for the population mean of all differences x−yx−y.

Answer 1

a)

dbar =-0.2857 (please take care of number of decimals as required in question)

b)sd =21.391

c)t = -0.0353

d)

positive critical value =2.447

e)

negative critical value =-2.447

f)

No

g)

for 95% CI; and 6 degree of freedom, value of t=			2.447
therefore confidence interval=sample mean -/+ t*std error
margin of errror          =t*std error=		19.783
lower confidence limit                     =		-20.0690
upper confidence limit                    =		19.4976
from above 95% confidence interval for population mean =(-20.069,19.498)