Question

In: Statistics and Probability

It was reported that 61​% of individual tax returns were filed electronically in 2012. A random...

It was reported that 61​% of individual tax returns were filed electronically in 2012. A random sample of 325 tax returns from 2013 was selected. From this​ sample,

233 were filed electronically.

a. Construct a 99​% confidence interval to estimate the actual proportion of taxpayers who filed electronically in 2013.

A 99​% confidence interval to estimate the actual proportion has a lower limit of __ and an upper limit of ___

Solutions

Expert Solution

We have given,                  
                  
x=233              
n=325              
Estimate for sample proportion=0.7169      
Level of significance is =1-0.99=0.01          
Z critical value(using Z table)=2.576          
                  
Confidence interval formula is                  


=(0.6525,0.7813)
                  
Lower limit for confidence interval=0.6525      
                  
Upper limit for confidence interval=0.7813      

A 99​% confidence interval to estimate the actual proportion has a lower limit of 65.25% and an upper limit of 78.13%


orchestra answered 2 years ago
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