Question

In: Statistics and Probability

The Internal Revenue Service sampled 20 tax returns and found that the average tax refund was...

The Internal Revenue Service sampled 20 tax returns and found that the average tax refund was $425.39 with a standard deviation of $107.10.

Construct a 99% confidence interval for the mean value of all tax refunds. Why do we have a use a t-confidence interval instead of a z-confidence interval for this problem?

Solutions

Expert Solution

Sample less than 30 and also population standard deviation not known/given.

We have given that,                  
                  
Sample mean =$425.39          
Sample standard deviation =$107.1      
Sample size =20          
Level of significance=1-0.99=0.01          
Degree of freedom =19          
                  
t critical value is (by using t table)=   2.861          
                  
Confidence interval formula is                   


=(356.87, 493.91)              
                  
                  
Lower confidence limit=   $356.87          
                  
Upper confidence limit=   $493.91          
                  

orchestra answered 2 years ago
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