Question

Bodrum and Marmaris seawater temperatures in the summer months are wanted to be compared. For this purpose, as a result of a 40-day examination, the average seawater temperature in Bodrum was 25°C, its variant was 16, and the seawater temperature was calculated as 27° C and its variant was 25 as a result of a 50-day examination in Marmaris. Test and interpret whether the average of seawater temperatures is equal to each other at α = 0.05 importance level. (C: H0 Cannot Be Red)

Answer 1

Ho :   µ1 - µ2 =   0                  
Ha :   µ1-µ2 ╪   0                  
                          
Level of Significance ,    α =    0.05                  
                          
Sample #1   ---->   Bodrum
mean of sample 1,    x̅1=   25.00                  
standard deviation of sample 1,   s1 =    4.00                  
size of sample 1,    n1=   40                  
                          
Sample #2   ---->   Marmaris
mean of sample 2,    x̅2=   27.00                  
standard deviation of sample 2,   s2 =    5.00                  
size of sample 2,    n2=   50                  
                          
difference in sample means =    x̅1-x̅2 =    25.0000   -   27.0   =   -2.00  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    4.5838                  
std error , SE =    Sp*√(1/n1+1/n2) =    0.9724                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   -2.0000   -   0   ) /    0.97   =   -2.057
                          
Degree of freedom, DF=   n1+n2-2 =    88                  

p-value =        0.042664   (excel function: =T.DIST.2T(t stat,df) )              
Conclusion:     p-value <α , Reject null hypothesis                      
                          
There is enough evidence that average of seawater temperatures is different to each other.

  

Thanks in advance!

revert back for doubt

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