METROPOLITAN RESEARCH, INC.- a numerical approach.
... used = 95% Since this is a Large Sample sigma = s. For 95% Confidence, Interval = 73340.3 (+/-) (1.96 * 24898.72/(50^1/2)) = 73340.3 (+/-) 6901.6 = 66438.7 to 80241.8 miles MANAGERIAL INTERPRETATION: We can say with 95% confidence that the average no. of miles, driven before a transmission failure, lies between 66439 and 80242 miles. (3) IMPLICATION OF THIS STATISTICAL FINDING: The average values lying between 66439 and 80242 miles and also the standard deviation of 24898 suggest that there may be some vehicles which had a transmission failure at the lower side of the number of miles. (4) Sample Size for Margin of Error = 5000 miles Confidence = 95% Therefore, z = 1.96 N = (z^2)*(s^2)/(5000^2) => N = 95.26 = 96 (on moving to the next highest integer) Therefore, sample size for margin of error of 5000 miles = 96 Vehicles. (5) Other Information Preferred to Evaluate Transmission failures: 1) The data regarding of what the manufacturer considers as an early transmission failure. 2) Whether the data provided by the repair firm is from the transmission failures of the same manufacturer is not given. 3) Data about other problems in automobiles with transmissio...