Question

1. The U.S. Census Bureau conducts a study to determine the time needed to complete the short form. The Bureau surveys 200 people. The sample mean is 8.2 minutes, and the sample standard deviation is 2.2 minutes.

1. To calculate a confidence interval for this data, would you use a value from the Z distribution or the t distribution? Write a sentence to explain your choice. (4 points)

2. Calculate the 99% confidence interval for µ, the population mean time it takes to complete the short Census form. (10 points)

3. Write a sentence to interpret your confidence interval. (4 points)

4. If the Census Bureau were willing to settle for only a 90% confidence level for this problem, instead of 99%, what would happen to the width of the confidence interval? Write a sentence to describe what would happen. (4 points)

Answer 1

t distribution is used,

Level of Significance ,    α =    0.01          
degree of freedom=   DF=n-1=   199          
't value='   tα/2=   2.601   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   2.2/√200=   0.1556          
margin of error , E=t*SE =   2.6008   *   0.1556   =   0.4046
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    8.20   -   0.404583   =   7.7954
Interval Upper Limit = x̅ + E =    8.20   -   0.404583   =   8.6046
99%   confidence interval is (   7.80   < µ <   8.60   )
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width of CI will get decrease