Question

You wish to test the claim that the first population mean is greater than the second population mean at a significance level of α=0.002α=0.002.     

Ho:μ1=μ2
Ha:μ1>μ2

You obtain the following two samples of data.

Sample #1	Sample #2
61.3 55.4 65.4 65.4 65.7 51.0 61.4 61.8 59.4 56.6 60.7 52.0	62.4 24.3 37.2 1.5 42.2 53.5 35.9 65.9 48.3 17.8 49.8 42.6

1. What is the test statistic for this sample?
   
   test statistic =  Round to 4 decimal places.
   
2. What is the p-value for this sample?
   
   p-value =  Round to 4 decimal places.
   
3. The p-value is...
   • less than (or equal to) αα
   • greater than αα
   
   
4. This test statistic leads to a decision to...
   • reject the null
   • accept the null
   • fail to reject the null
   
   
5. As such, the final conclusion is that...
   • There is sufficient evidence to warrant rejection of the claim that the first population mean is greater than the second population mean.
   • There is not sufficient evidence to warrant rejection of the claim that the first population mean is greater than the second population mean.
   • The sample data support the claim that the first population mean is greater than the second population mean.
   • There is not sufficient sample evidence to support the claim that the first population mean is greater than the second population mean.

Answer 1

Ho :   µ1 - µ2 =   0                  
Ha :   µ1-µ2 >   0                  
                          
Level of Significance ,    α =    0.002                  
                          
Sample #1   ---->   sample 1                  
mean of sample 1,    x̅1=   59.68                  
standard deviation of sample 1,   s1 =    5.00                  
size of sample 1,    n1=   12                  
                          
Sample #2   ---->   sample 2                  
mean of sample 2,    x̅2=   40.12                  
standard deviation of sample 2,   s2 =    18.53                  
size of sample 2,    n2=   12                  
                          
difference in sample means =    x̅1-x̅2 =    59.6750   -   40.1   =   19.56  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    13.5721                  
std error , SE =    Sp*√(1/n1+1/n2) =    5.5408                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   19.5583   -   0   ) /    5.54   =   3.5299
                          
Degree of freedom, DF=   n1+n2-2 =    22                  

p-value =        0.0009 [excel function: =T.DIST.RT(t stat,df) ]             
Conclusion:     p-value <α , Reject null hypothesis              

The sample data support the claim that the first population mean is greater than the second population mean.

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THANKS

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