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In: Statistics and Probability

The following information was obtained from independent random samples. The Degrees of Freedom have be calculated...

The following information was obtained from independent random samples. The Degrees of Freedom have be calculated to be 19. The Standard Deviations are Unknown.
Small Sample Size: Use t-value
Sample 1 Sample 2
Sample Mean 45 42
Sample Variance 85 90
Sample Standard Deviation
Sample Size 10 12
Standard Error
Confidence Coefficient 0.95
Level of Significance
Degrees of Freedom 19
t-value
Margin of Error
Point Estimate of Difference 3
Lower Limit
Upper Limit
The 95% confidence interval for the difference between the two population means is
to

Solutions

Expert Solution

Degree of freedom, DF=       19          
t-critical value =    t α/2 =    2.093   (excel formula =t.inv(α/2,df)      
                  
                  
                  
std error , SE =    √(s1²/n1+s2²/n2) =    4.000          
margin of error, E = t*SE =    2.093   *   4.000   =   8.3721
                  
difference of means = x̅1-x̅2 =    45.0000   -   42.000   =   3.0000
confidence interval is                   
Interval Lower Limit = (x̅1-x̅2) - E =    3.0000   -   8.372   =   -5.3721
Interval Upper Limit = (x̅1-x̅2) + E =    3.0000   -   8.372   =   11.3721

CI (-5.3721 , 11.3721)

...................


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