Question

Consider the following hypothesis statement using a = 0.05 and data from two independent samples. Assume the population variances are not equal and the populations are normally distributed. H0: u1 - u2 = 0 H1: u1 - u2 = 0 x1: = 114.7 x2 = 122.0 s1 = 24.6 s2 = 14.3 n1 = 14 n2 20 a. Calculate the appropriate test statistic and interpret the result. b. Approximate the p-value using Table 5 in Appendix A and interpret the results. c. Determine the precise p-value using Excel. d. Verify your results using PHStat..

Answer 1

Ho :   µ1 - µ2 =   0          
Ha :   µ1-µ2 ╪   0         
                  
Level of Significance ,    α =    0.05          
                  
Sample #1   ---->   sample 1          
mean of sample 1,    x̅1=   114.70          
standard deviation of sample 1,   s1 =    24.6          
size of sample 1,    n1=   14          
                  
Sample #2   ---->   sample 2          
mean of sample 2,    x̅2=   122.000          
standard deviation of sample 2,   s2 =    14.30          
size of sample 2,    n2=   20          
                  
difference in sample means = x̅1-x̅2 =    114.700   -   122.0000   =   -7.3000
                  
std error , SE =    √(s1²/n1+s2²/n2) =    7.3110          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   -7.3000   /   7.3110   ) =   -0.998
                  
  = 19          
                  
                  
  
  
p-value =        0.3306   (excel function: =T.DIST.2T(t stat,df) )  

   
Conclusion:     p-value>α , Do not reject null hypothesis              
.........................

Please revert back in case of any doubt.

Please upvote. Thanks in advance.