Question

Researchers measured the data speeds for a particular smartphone carrier at 50 airports. The highest speed measured was 77.6 Mbps. The complete list of 50 data speeds has a mean of x overbarequals17.52 Mbps and a standard deviation of sequals21.76 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?

Answer 1

a. Difference between​ carrier's highest data speed and the mean of all 50 data​ speeds = 77.6 - 17.52 = 60.08

b. Standard deviations = 60.80 / 21.76 = 2.76

2.76 standard deviations is that​ [the difference found in part​ (a)]

c. Z-score for carrier's highest data speed = ( X - mean ) / Standard deviation = (77.6 - 17.52) / 21.76 = 2.76

d. Since Z -score = 2.76 does not lie between - 2 and 2 , we can say that the carrier's highest data speed​ is significant.