A major car manufacturer wants to test a new engine to determine whether it meets new air pollution standards. The mean emission µ of all engines of type must be less than 20 parts per million of carbon. Ten engines are manufactured for testing purposes and the emission level of each is determined. The data (in parts per million) are listed below: 15.6 16.2 22.5 20.5 16.4 19.4 16.6 17.9 12.7 13.9 Do the data supply sufficient evidence to allow the manufacturer to conclude that this type of engine meets the pollution standard? Use a significance level of 5%.
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.
- A major car manufacturer wants to test a new engine to determine whether it meets new air pollution standards. The
mean emission µ of all engines of type must be less than 20 parts per million of carbon. Ten engines are manufactured for testing purposes and the emission level of each is determined. The data (in parts per million) are listed below:
15.6 16.2 22.5 20.5 16.4 19.4 16.6 17.9 12.7 13.9
Do the data supply sufficient evidence to allow the manufacturer to conclude that this type of engine meets the pollution standard? Use a significance level of 5%.
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