Question

Hypothesis Testing and Confidence Intervals for Proportions and Hypothesis Test for Difference between Two Means

A pharmaceutical company is testing a new cold medicine to determine if the drug has side affects. To test the drug, 8 patients are given the drug and 9 patients are given a placebo (sugar pill). The change in blood pressure after taking the pill was as follows:

Given drug: 3 4 5 1 -2 3 5 6

Given placebo: 1 -1 2 7 2 3 0 3 4

Test to determine if the drug raises patients’ blood pressure more than the placebo using  = 0.01

Answer 1

Ho :   µ1 - µ2 =   0                  
Ha :   µ1-µ2 >   0                  
                          
Level of Significance ,    α =    0.01                  
                          
Sample #1   ----> drug
mean of sample 1,    x̅1=   3.125                  
standard deviation of sample 1,   s1 =    2.588                  
size of sample 1,    n1=   8                  
                          
Sample #2   ----> placebo   
mean of sample 2,    x̅2=   2.333                  
standard deviation of sample 2,   s2 =    2.345                  
size of sample 2,    n2=   9                  
                          
difference in sample means =    x̅1-x̅2 =    3.1250   -   2.3   =   0.792  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    2.4614                  
std error , SE =    Sp*√(1/n1+1/n2) =    1.1960                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   0.7917   -   0   ) /    1.20   =   0.662
                          
Degree of freedom, DF=   n1+n2-2 =    15                  
p-value =        0.259031   [excel function: =T.DIST.RT(t stat,df) ]              
Conclusion:     p-value>α , Do not reject null hypothesis                      
                          
There is not enough evidence to conclude that drug raises patients’ blood pressure more than the placebo