The supervisor of an orange juice-bottling company is considering the purchase of a new machine to bottle 16-fluid-ounce (473-milliliter) bottles of 100% pure orange juice and wants an estimate of the difference in the mean filling weights between the new machine and the old machine. Random samples of bottles of orange juice that had been filled by both machines were obtained. Estimate the difference in the mean filling weights between the new and the old machines? Dis- cuss the assumptions. Use α = 0.10. New Machine Old MachineMean 470 milliliters 460 millilitersStandard deviation 5 milliliters 7 millilitersSample size 15 12
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 supervisor of an orange juice-bottling company is considering the purchase of a new machine to bottle 16-fluid-ounce (473-milliliter) bottles of 100% pure orange juice and wants an estimate of the difference in the mean filling weights between the new machine and the old machine. Random samples of bottles of orange juice that had been filled by both machines were obtained. Estimate the difference in the mean filling weights between the new and the old machines? Dis- cuss the assumptions. Use α = 0.10.
New Machine Old Machine
Mean 470 milliliters 460 milliliters
Standard deviation 5 milliliters 7 milliliters
Sample size 15 12
Given
The data is as follows:
| New machine | Old machine | |
| Mean | ||
| Standard deviation | ||
| Sample size |
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