Question

We wish to see if, on average, traffic is moving at the posted speed limit of 65 miles per hour along a certain stretch of Interstate 70. On each of four randomly selected days, a randomly selected car is timed and the speed of the car is recorded. The observed sample mean speed is 70 mph and the sample standard deviation is 4.08 mph. Assume that speeds are normally distributed with mean μ. Which of the following is the 95% confidence interval for μ, the population mean speed on the stretch of Interstate 70.

Question 11 options:

(66.00, 74.00)

(66.75, 73.25)

(63.51, 76.49)

(67.96, 72.04)

Answer 1

sample std dev ,    s =    4.0800
Sample Size ,   n =    4
Sample Mean,    x̅ =   70.0000
Level of Significance ,    α =    0.05          
degree of freedom=   DF=n-1=   3          
't value='   tα/2=   3.1824   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   4.0800   / √   4   =   2.040000
margin of error , E=t*SE =   3.1824   *   2.04000   =   6.492190
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    70.00   -   6.492190   =   63.507810
Interval Upper Limit = x̅ + E =    70.00   -   6.492190   =   76.492190
95%   confidence interval is (   63.51   < µ <   76.49   )

option (c)

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

THANKS

revert back for doubt

please upvote