Example 3: Alexis has a lengthy commute to work each day. There are two main routes that she takes on her way to work and they both average 40 minutes. Alexis likes to be able to predict how long before work she needs to leave in order to make it on time, and since both routes take the same average amount of time, she was interested in determining whether or not one route was more consistent with its timing. So she recorded how long it took her to drive to work 20 times total (Data shown below). Carry out an appropriate hypothesis test at the a = to determine if one route yields more consistent times than the other. 0.05 level %3D Route 1 41 42 41.5 40.5 41 40.5 40 39 40 42 Route 2 37 36 39 38 37 40 44 41 43 38 Standard Deviation Sample Size Route 1 0.950 10 Route 2 2.669 10
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.
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