.Construct the 95% confidence intervals for the population variance and standard deviation b.Test at a 2.5% significance level whether the variance of the particle diameters of all particles in 220-rated sandpaper is greater than 2.0 micrometers
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.
3. Sandpaper is rated by the coarseness of the grit on the paper. Sandpaper that is more coarse will remove material faster. Jobs that involve the final sanding of bare wood prior to painting or sanding in between coats of paint require sandpaper that is much finer. A manufacturer of sandpaper rated 220, which is used for the final preparation of bare wood, wants to make sure that the variance of the diameter of the particles in their 220 sandpaper does not exceed 2.0 micrometers. Fifty-one randomly selected particles are measured. The variance of the particle diameters is 2.13 micrometers. Assume that the distribution of particle diameter is approximately normal.
a.Construct the 95% confidence intervals for the population variance and standard deviation
b.Test at a 2.5% significance level whether the variance of the particle diameters of all particles in 220-rated sandpaper is greater than 2.0 micrometers
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