Info: Ho:1 = 2 H1:1 > 2 n1 = n2 = 15 xbar1 = 7.7 xbar2 = 5.7 s1^2 = 4 s2^2 = 9 A
ID: 2958163 • Letter: I
Question
Info:
Ho:1 = 2
H1:1 > 2
n1 = n2 = 15
xbar1 = 7.7
xbar2 = 5.7
s1^2 = 4
s2^2 = 9
Assume equal variance
=0.05
Questions:
a.) Do you accept or reject the null hypothesis and what is the P-Value?
b.) What is the power of the test in part a if 1 is 3 units greater than 2?
c.) Assuming equal sample sizes, what should the sample size be to obtain =0.05 if 1 is 3.1 units greater than 2? Assume =0.05.
My attempt:
a.)I calculated a pooled variance of 2.14834, said that we should reject the null because the p-value is somewhere between 0.01 and 0.025. I can't get an exact number for the P-value but I need it. How do I get???
b and c.) I calculated the power to be 0.933 and the sample size to be 16. Are these correct?
PARTS B AND C ARE CORRECT AND THE NULL HYPOTHESIS IS REJECTED. THE ONLY THING I CAN'T FIGURE OUT IS HOW TO CALCULATE THE EXACT P-VALUE.
Explanation / Answer
Since you've already calculated part b and c, I will try to explain part a.
The Test Statistic for a paired T Test is given by the following equation:
t=(xd-hypothesized value)/(sd/n) where the test is based on df=n-1
Ho:1 = 2
H1:1 > 2
n1 = n2 = 15
xbar1 = 7.7 xd=(x1-x2) sd=(s1-s2)
xbar2 = 5.7
s1^2 = 4 s1=2
s2^2 = 9 s2=3
xd=(7.7-5.7)=2
sd=(2-3)=-1
t=(2)-0/(-1/15)=-2/.2582=-7.75 with df=14
The pvalue of a test statistic of -7.75 and degrees of freedom of 14 is 0
p value0 =.05
Since 0<.05, The null hypothesis is rejected
I hope this helped!
Cheers!