A researcher has developed a new drug designed to reduce blo

A researcher has developed a new drug designed to reduce blood pressure. In an experiment, 21 researchers were assigned randomly to the treatment group and received the new experimental drug. The other 23 subjects were assigned to the control group and received a standard, well-known treatment. After a suitable period, the reduction in blood pressure for each subject was recorded. A summary of these data is:

Treatment group                                                n=21             xbar=23.48           s=8.01

Control group                                                     n=23             xbar=18.52           s=7.15

The researcher suspects that the new drug results in greater average reduction in blood pressure than the old drug does. Based on these data, the computed two-sample t statistic is:

a. 1.84

b. 2.31

c. 2.16

d. 4.70

Solution

  
Calculating the means of each group,              
              
X1 =    23.48          
X2 =    18.52          
              
Calculating the standard deviations of each group,              
              
s1 =    8.01          
s2 =    7.15          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    21          
n2 = sample size of group 2 =    23          

Thus, df = n1 + n2 - 2 =    42          

Also, sD =    2.297381172          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    2.158979999 = 2.16 [ANSWER, OPTION C]