The manager of a fleet of automobiles is testing two brands of radial tires. She assigns one tire of each brand at random to the two rear wheels of eight cars and runs the cars until the tires wear out. The data are shown here (in km). Find a 99% CI on the difference in mean life. Which brand would you prefer, based on this calculation? Car Brand 1 Brand 2 1 36925 34318 2 45300 42280 3 36240 35500 4 32100 31950 5 37210 38015 6 48360 47800 7 38200 37810 8 33500 33215
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 manager of a fleet of automobiles is testing two brands of radial tires. She assigns one tire of each brand at random to the two rear wheels of eight cars and runs the cars until the tires wear out. The data are shown here (in km). Find a 99% CI on the difference in mean life. Which brand would you prefer, based on this calculation?
| Car | Brand 1 | Brand 2 |
| 1 | 36925 | 34318 |
| 2 | 45300 | 42280 |
| 3 | 36240 | 35500 |
| 4 | 32100 | 31950 |
| 5 | 37210 | 38015 |
| 6 | 48360 | 47800 |
| 7 | 38200 | 37810 |
| 8 | 33500 | 33215 |
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
