The gasoline price often varies a great deal across different regions across country X. The following data show the price per gallon for regular gasoline for a random sample of gasoline service station for three major brands of gasoline (A, B and C) located in 10 metropolitan areas across the country X. (Left or right tail).
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.
The gasoline price often varies a great deal across different regions across country X. The following data show the price per gallon for regular gasoline for a random sample of gasoline service station for three major brands of gasoline (A, B and C) located in 10 metropolitan areas across the country X.
(Left or right tail).
|
A |
B |
C |
|
3.77 |
3.83 |
3.78 |
|
3.72 |
3.83 |
3.87 |
|
3.87 |
3.85 |
3.89 |
|
3.76 |
3.77 |
3.79 |
|
3.83 |
3.84 |
3.87 |
|
3.85 |
3.84 |
3.87 |
|
3.93 |
4.04 |
3.99 |
|
3.79 |
3.78 |
3.79 |
|
3.78 |
3.84 |
3.79 |
|
3.81 |
3.84 |
3.86 |
a State the null and alternative hypothesis for single factor ANOVA to test for any significant difference in the
B State the decision rule at 5% significance level.
C Calculate the test statistic.
d Based on the calculated test statistics decide whether any significant difference in the mean price of gasoline for three bands.
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