A soda manufacturer is interested in determining whether its bottling machine tends to overfill. Each bottle is supposed to contain 12 oz of fluid. A random sample of size 36 is taken from bottles coming off the production line, and the contents of each bottle are carefully measured. It is found that the mean amount of soda for the sample of bottles is 12.1 oz. Suppose that the standard error for the mean amount of soda is 0.08. (1) What is the population parameter of interest in this study? Give a point estimate for the population parameter. (2) Give a 95% confidence interval for the population parameter and interpret the confidence interval. (3) Is the machine overfilling? Explain.
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 soda manufacturer is interested in determining whether its bottling machine tends to
overfill. Each bottle is supposed to contain 12 oz of fluid. A random sample of size 36 is taken
from bottles coming off the production line, and the contents of each bottle are carefully
measured. It is found that the
that the standard error for the mean amount of soda is 0.08.
(1) What is the population parameter of interest in this study? Give a point estimate for the
population parameter.
(2) Give a 95% confidence interval for the population parameter and interpret the confidence
interval.
(3) Is the machine overfilling? Explain.
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