Question
In: Statistics and Probability
Researchers measured the data speeds for a particular smartphone carrier at 50 airports. The highest speed...
Researchers measured the data speeds for a particular smartphone carrier at 50 airports. The highest speed measured was 71.7 Mbps. The complete list of 50 data speeds has a mean of x overbarequals18.12 Mbps and a standard deviation of sequals17.45 Mbps. a. What is the difference between carrier's highest data speed and the mean of all 50 data speeds? b. How many standard deviations is that [the difference found in part (a)]? c. Convert the carrier's highest data speed to a z score. d. If we consider data speeds that convert to z scores between minus2 and 2 to be neither significantly low nor significantly high, is the carrier's highest data speed significant?
Solutions
Expert Solution
The highest speed measured was 71.7 Mbps.
The complete list of 50 data speeds has a mean 
= 18.12 Mbps and a standard deviation 
= 17.45 Mbps.
The difference between carrier's highest data speed and the mean of all 50 data speeds = (71.7-18.12) Mbps = 53.58 Mbps
53.58/17.45 
3.07 which implies that the difference between
carrier's highest data speed and the mean of all 50 data speeds is
approximately 3.07 standard deviations
The z-score of the carrier's highest data speed =
(71.7-)/
= (71.7-18.12)/17.45
3.07
If we consider data speeds that convert to z scores between -2 and 2 to be neither significantly low nor significantly high, the carrier's highest data speed is significant as it is approximately 3.07 and does not belong to the interval (-2,2).
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