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Researchers measured the data speeds for a particular smartphone carrier at 50 airports. The highest speed measured was 75.6 Mbps. The complete list of 50 data speeds has a mean of x overbar equals 15.62 Mbps and a standard deviation of s equal s 20.03 Mbps.
Researchers measured the data speeds for a particular smartphone carrier at 50 airports. The highest speed measured was 75.6 Mbps. The complete list of 50 data speeds has a mean of x overbar equals 15.62 Mbps and a standard deviation of s equal s 20.03 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 minus 2 and 2 to be neither significantly low nor significantly high, is the carrier's highest data speed significant?
Answer:a) 59.98b) 2.99c) 2.99d) Significantly HighStep-by-step explanation:Part a)Highest speed measured = x = 75.6 MbpsAverage/Mean speed == 15.62 MbpsStandard Deviation = s = 20.03 MbpsWe need to find the difference between carrier's highest data speed and the mean of all 50 data speeds i.e. x -x -= 75.6 - 15.62 = 59.98 MbpsThus, the difference between carrier's highest data speed and the mean of all 50 data speeds is 59.98 MbpsPart b)In order to find how many standard deviations away is the difference found in previous part, we divide the difference by the value of standard deviation i.e.This means, the difference is2.99 standard deviationsor in other words we can say, the Carrier's highest data speed is 2.99 standard deviations above the mean data speed.Part c)A z score tells us that how many standard deviations away is a value from the mean. We calculated the same in the previous part. Performing the same calculation in one step:The formula for the z score is:Using the given values, we get:Thus, the Carriers highest data is equivalent to a z score of 2.99Part d)The range of z scores which are neither significantly low nor significantly high is-2 to + 2. The z scores outside this range will be significant.Since, the z score for carrier's highest data speed is2.99which is well outside the given range, i.e. greater than 2, we can conclude that the carrier's highest data speed issignificantly higher....