Question

4. The following table summarizes the sucrose consumption (mg in 30 min) of black blowflies injected with Pargyline or saline (control) 905 Sample 1 (control) Sample 2 900 14.9 46.5 5.4 11.7 Use hypothesis testing to test whether there is strong evidence that the sucrose con- sumption of black blowflies is indeed larger when injected with Pargyline compared to saline (control)?. Use a 0.05. In this problem, find the critical value or P-value using R. (no need to include the Routput here).

Answer 1

Ho :   µ1 - µ2 =   0          
Ha :   µ1-µ2 <   0          
                  
Level of Significance ,    α =    0.05          
                  
Sample #1   ---->   1          
mean of sample 1,    x̅1=   14.90          
standard deviation of sample 1,   s1 =    5.4          
size of sample 1,    n1=   900          
                  
Sample #2   ---->   2          
mean of sample 2,    x̅2=   46.500          
standard deviation of sample 2,   s2 =    11.70          
size of sample 2,    n2=   905          
                  
difference in sample means = x̅1-x̅2 =    14.900   -   46.5000   =   -31.6000
                  
std error , SE =    √(s1²/n1+s2²/n2) =    0.4286          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   -31.6000   /   0.4286   ) =   -73.7361
                  
Degree of freedom, = 1273          
                  
                  
\p-value =        0.0000   [ excel function: =T.DIST(t stat,df) ]       
Conclusion:     p-value<α , Reject null hypothesis              
                  
There is enough evidence to support the claim