The variance in a production process is an important measure of the quality of the process. A large variance often signals an opportunity for improvement in the process by finding ways to reduce the process variance. Machine 1 Machine 2 2.95 3.45 3.50 3.75 3.48 3.26 3.33 3.20 3.22 3.30 3.34 3.28 3.29 3.25 3.30 | 3.26 3.16 3.20 3.22| 3.38 | 3.90 3.36 3.25 3.28 3.38 3.34 3.35 3.19 3.35 3.05 3.36 3.28 3.20 3.22 2.98 3.45 3.70 3.34 3.18 3.35 3.30 3.28 3.30 3.20 3.16 3.33 3.12 Conduct a statistical test to determine whether there is a significant difference between the variances in the bag weights for two machines. Use a 0.05 level of significance. What is your conclusion? State the null and alternative hypotheses. Hoi o,? > a,? Hoio,? = 02
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.
Level of significance = = 0.05
Given data is,
| Machine 1 | Machine 2 |
| 2.95 | 3.22 |
| 3.45 | 3.3 |
| 3.5 | 3.34 |
| 3.75 | 3.28 |
| 3.48 | 3.29 |
| 3.26 | 3.25 |
| 3.33 | 3.3 |
| 3.2 | 3.26 |
| 3.16 | 3.38 |
| 3.2 | 3.3 |
| 3.22 | 3.35 |
| 3.38 | 3.19 |
| 3.9 | 3.35 |
| 3.36 | 3.05 |
| 3.25 | 3.36 |
| 3.28 | 3.28 |
| 3.2 | 3.3 |
| 3.2 | 3.28 |
| 2.98 | 3.3 |
| 3.45 | 3.2 |
| 3.7 | 3.16 |
| 3.34 | 3.33 |
| 3.18 | |
| 3.35 | |
| 3.12 |
We have to conduct a statistical test to determine whether there is significant difference between the variances in the bag weights of two machines.
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