ONE-FACTOR ANALYSIS OF VARIANCE > Example 2: An investigator for a consumer cooperative organized a study of the mileages obtainable from three different brands of gasoline. Using 15 identical motors set to run at the same speed, the investigator randomly assigned each brand of gasoline to 5 of the motors. Each of the motors was then run on 10 gallons of gasoline, with the total mileages obtained as follows Gas 2 Gas 1 Gas 3 220 251 226 246 244 235 232 242 252 272 250 260 266 Test the hypothesis that the average mileage obtained is the same for all three types of gasoline. Use the 5 percent level of significance. 18
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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