Commuting A man who moves to a new city sees thatthere are two routes he could take to work. A neighborwho has lived there a long time tells him Route A willaverage 5 minutes faster than Route B. The man decidesto experiment. Each day he flips a coin to determinewhich way to go, driving each route 20 days. He finds that Route A takes an average of 40 minutes, with stan-dard deviation 3 minutes, and Route B takes an aver-age of 43 minutes, with standard deviation 2 minutes. Histograms of travel times for the routes are roughlysymmetric and show no outliers.a) Find a 95% confidence interval for the difference inaverage commuting time for the two routes.b) Should the man believe the old-timer’s claim that he can save an average of 5 minutes a day by always driv-ing Route A? Explain.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
there are two routes he could take to work. A neighbor
who has lived there a long time tells him Route A will
average 5 minutes faster than Route B. The man decides
to experiment. Each day he flips a coin to determine
which way to go, driving each route 20 days. He finds
dard deviation 3 minutes, and Route B takes an aver-
age of 43 minutes, with standard deviation 2 minutes.
symmetric and show no outliers.
a) Find a 95% confidence interval for the difference in
average commuting time for the two routes.
b) Should the man believe the old-timer’s claim that he
ing Route A? Explain.
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