Question

An Anesthesiologist claims that a certain medication decreases the pain level of post-operative patients within 20 minutes. Fourteen Patients are randomly chosen and asked to give a number from 1-10 that represents his/her pain level as soon as waking up from surgery and then again in 20 minutes after taking the medication. The pain level for patients before and after the medication is recorded below.  Assume the pain levels are normally distributed. Use 0.05 as the level of significance, as well as d indicates the mean difference: patient pain level before medication -  patient pain level after medication.

Chose the appropriate hypotheses set up for this situation.

Patient Pain Level	1	2	3	4	5	6	7	8	9	10	11	12	13	14
Pain Level Before Medication	8	10	9	6	3	8	7	5	4	10	8	5	7	9
Pain Level After Medication	7	5	1	3	5	7	4	8	6	9	7	1	9	8

Based on your choice in part 1 , determine the direction of your hypothesis test.

Right skewed test.

Right-tailed test.

Left-tailed test.

Two-tailed test.

Calculate the test statistics.

Calculate the P-Value for this test statistic.

(Round your answer to 4 decimal places)

Based on your finding in part 4, what would be the appropriate decision?

Accept the null hypothesis.
		Fail to Reject the alternative hypothesis.
		Reject the alternative hypothesis.
		Fail to Reject the null hypothesis.
		Reject the null hypothesis.

Based on your finding from part 5,

a.) What type of error could have occurred potentially?

b.) Explain the reasoning of the type of error of your choice.

Based on your findings from previous parts (1-5), which one of the statements below would be true?

The data does not support the anesthesiologist’s claim that the medication given to patients after surgery reduces pain within 20 minutes.
		The data supports the anesthesiologist’s claim, but not enough to conclude that the medication given to patients after surgery reduces pain within 20 minutes.
		The data supports the anesthesiologist's  claim that the medication given to patients after surgery reduces pain within 20 minutes.

Answer 1

Right-tailed test.

Ho :   µd=   0
Ha :   µd >   0
======================

SAMPLE 1	SAMPLE 2	difference , Di =sample1-sample2	(Di - Dbar)²
8	7	1	0.128
10	5	5	13.270
9	1	8	44.128
6	3	3	2.699
3	5	-2	11.270
8	7	1	0.128
7	4	3	2.699
5	8	-3	18.985
4	6	-2	11.270
10	9	1	0.128
8	7	1.000	0.128
5	1	4.000	6.985
7	9	-2.000	11.270
9	8	1.000	0.128

mean of difference ,    D̅ =ΣDi / n =   1.3571                  
                          
std dev of difference , Sd =    √ [ (Di-Dbar)²/(n-1) =    3.0786                  
                          
std error , SE = Sd / √n =    3.0786   / √   14   =   0.8228      
                          
t-statistic = (D̅ - µd)/SE = (   1.357142857   -   0   ) /    0.8228   =   1.649
                          
Degree of freedom, DF=   n - 1 =    13                        
                          
p-value =        0.0615   [excel function: =t.dist.rt(t-stat,df) ]               
Decision:   p-value>α , Fail to reject null hypothesis                      
-=================

a) Type II error could have been occucred

b) Type II error is fail to reject false null hypothesis

The data does not support the anesthesiologist’s claim that the medication given to patients after surgery reduces pain within 20 minutes.