The followings are the questions I have trouble to answer. I am appreciated your
ID: 3222178 • Letter: T
Question
The followings are the questions I have trouble to answer. I am appreciated your help. May I ask if you provide a step by step explanation, please? Thanks!
1.
For some two-factor factorial exp eriment with two ( 2) observations for
each factor-level combinations, where factor A has 3 levels and factor
B has 6 levels, we are asked to test for factor interaction. Find the
rejection region for this test based on the 0.01 level.
(a) F > 3.51
(b) F > 3.08
(c) F > 6.01
(d) F > 8.40
2.
Consider the following summary statistics for data obtained in a simple
linear regression problem:
n = 23, s 2 = 561.088, SSxx = 151.086, ˆ 1 = 4.4285.
We use t-test to test H0 : 1 = 0 vs. Ha : 1 > 0. Find the observed
value of the test statistic. (Hint: Use the formula given on page 572.)
(a) 4.4285
(b) 10.5308
(c) 1.1925
(d) 2.2980
3.
In fitting a least squares line to 11 data points, we obtain
SS
xx = 67, SSy y = 95, SSxy = 50.
We then use t-test to test H0 : = 0 vs. Ha : 6= 0. Find the
observed value of the test statistic. (Hint: Use the formula given on
page 582.)
(a) 1.8801
(b) 2.4128
(c) 0.6267
(d) 0.0639
Explanation / Answer
Question-1
Degree of freedom for intraction =(3-1)*(6-1)=10
Sample size n=3*6*2=36
Error degree of freedom = 3*6*(2-1)=18
So Degree of freedom for interaction effect F-statistic =(10,18)
So, critical F=3.51 using excel function =FINV(0.01,10,18)
Hence, part-a is answer
Question-2
Standard error of slope = sqrt(s2/SSxx) =sqrt(561.088/151.086)=1.9271
So, test statistic t= beta1/SE(beta1)
=4.4285/1.9271
=2.2980
So, option-d is answer
Question-3:
Sample correlation r= SSxy/sqrt(SSxx*SSyy)
=50/sqrt(67*95)
=0.6267
So, t=r*sqrt(n-2)/sqrt(1-r2)
=0.6267*sqrt(11-2)/sqrt(1-0.6267*0.6267)
=2.4127
So,option-b is asnswer
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.