Question 1179107: I could really use the help! Thank you!!
An experimental surgical procedure is being studied as an alternative to the old method. Both methods are considered safe. Seven Surgeons perform the operation on two patients matched by age, sex and other relevant factors, with the results shown below. The time to complete the surgery (in minutes) was recorded. (a) at the 5 percent significance level, is the new way faster? State your hypotheses and show all steps clearly. (b) Is the decision close?
...........Old Way | New Way
Surgeon 1...36 | 29
Surgeon 2...55 | 42
Surgeon 3...28 | 30
Surgeon 4...40 | 32
Surgeon 5...62 | 56
Surgeon 6...40 | 40
Surgeon 7...44 | 45
1. State the null and alternative hypothesis (you MUST label which is H0 and which is H1)
2. What is the critical value?
3. What is the test statistic?
4. Do you reject or fail to reject?
5. Is the decision close? (*one way to approach this is to see if the decision is sensitive to alpha*)
5a. If you answered yes, why? If you answered no, why not?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Use a paired t-test and the differences between x2 and x1
old way=x1
new way=x2
if experiment works, x2 will be < x1 units minutes
so Ho: x2 > =x1 It took longer to do or was the same
Ha: x2 < x1 It didn't take longer to do
or x2-x1 is < =0
alpha=0.05 p{reject Ho|Ho true}
test is a paired t df=6,0.95, 1 way
critical value is t=-1.943
look at differences, which are -7,-13,+2,-8,-6,0,+1
=-31
x bar=-4.43
s=5.56
t=-4.43/5.56/sqrt(7)
=-4.43*sqrt(7)/5.56=--2.107
reject Ho, since -2.107< -1.943, p-value =0.04
It is a slightly close decision
But conclusion is to reject Ho. Alpha and 1 or 2 way tests must be set up in advance and not added in later to manipulate the answer in a specific direction.
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