Question

HW09: Problem 3 Problem Value: 3 point(s). Problem Score: 0%. Attempts Remaining: 3 attempts. (3 points) The Highway Safety Department wants to study the driving habits of individuals. A sample of 26 cars traveling on a particular stretch of highway revealed an average speed of 67.3 miles per hour with a standard deviation of 6.1 miles per hour. Round to 4 decimal places. 1.Calculate a 99% confidence interval for the true mean speed of all cars on this particular stretch of highway. 2. What sample size is needed to estimate the true average speed to within 1.5 mph at 99% confidence? Note: For consistency's sake, round your t* value to 3 decimal places before calculating the necessary sample size Choose n

Answer 1

1)

Level of Significance ,    α =    0.01          
degree of freedom=   DF=n-1=   25          
't value='   tα/2=   2.7874   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   16.0000   / √   26   =   3.1379
margin of error , E=t*SE =   2.7874   *   3.1379   =   8.7466
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    67.30   -   8.746578   =   58.5534
Interval Upper Limit = x̅ + E =    67.30   -   8.746578   =   76.0466
99%   confidence interval is (   58.55   < µ <   76.05   )

2)

Standard Deviation , s =    6.1                  
sampling error ,    E =   1.5                  
Confidence Level ,   CL=   99%                  
                          
alpha =   1-CL =   1%                  
Z value =    Zα/2 =    2.576   [excel formula =normsinv(α/2)]              
                          
Sample Size,n = (Z * s/ E )² = (   2.576   *   6.1   /   1.5   ) ² =   109.726
                          
                          
So,Sample Size needed=       110