Question

• Question 25

	Problem Set 2: Independent Samples T-Test Use the following information to answer questions 25-27: The Tronderlag Foundation, a research think tank based in Norway, has asked your advice in regard to a matter involving inferential statistics. The foundation has studied the dependency that Scandinavian and Southern European countries have on exports for their Gross Domestic Product. The foundation collected data on five Scandinavian countries and six Southern European countries regarding the percentage of GDP that is derived from export sales. The foundation analysts have “eyeballed” the GDP data and believe “in their gut” that there is a statistically significant difference between the two independent samples. Is their gut reaction correct? What is the formula for the Independent Samples t-test?

• Question 26

	Assess the Tronderlag Foundation gut instinct by performing an independent samples t-test on these two datasets. Show your work at each step. Round the results of your calculations to two decimal places at each step. Use the following table of information in your calculations (WORTH 10 POINTS). World Region % of GDP from Exports Standard Deviation of % of GDP from Exports N Scandanavia (X1) 60.3 6.22 5 Southern Europe (X2) 52.9 9.32 6 t = _________

• Question 27

	Do you reject or accept the null hypothesis for this Independent Samples t-test? Briefly explain.

Answer 1

Ho :   µ1 - µ2 =   0                  
Ha :   µ1-µ2 ╪   0                  
                          
Level of Significance ,    α =    0.01                  
                          
Sample #1   ---->   Scandanavia
mean of sample 1,    x̅1=   60.30                  
standard deviation of sample 1,   s1 =    6.22                  
size of sample 1,    n1=   5                  
                          
Sample #2   ---->   Southern Europe
mean of sample 2,    x̅2=   52.90                  
standard deviation of sample 2,   s2 =    9.32                  
size of sample 2,    n2=   6                  
                          
difference in sample means =    x̅1-x̅2 =    60.3000   -   52.9   =   7.40  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    8.0902                  
std error , SE =    Sp*√(1/n1+1/n2) =    4.8989                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   7.4000   -   0   ) /    4.90   =   1.511

2)

                          
Degree of freedom, DF=   n1+n2-2 =    9                  
  
p-value =        0.165186   (excel function: =T.DIST.2T(t stat,df) )              
Conclusion:     p-value>α , Do not reject null hypothesis             

There is a statistically no significant difference between the two independent samples. their gut reaction is not correct.

       

Thanks in advance!

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