A certain reaction was run several times using each of the two catalysts, A and B. The catalysts were supposed to control the yield of an undesirable side product. Results, in units of percentage yield, for 24 runs of catalyst A and 20 runs of catalyst B are as follows: Catalyst A Catalyst B 4.4 3.4 2.6 3.8 3.4 1.1 2.9 5.5 4.9 4.6 5.2 4.7 6.4 5.0 5.8 2.5 4.1 2.6 6.7 4.1 3.7 3.8 3.1 1.6 3.6 2.9 2.6 4.0 3.5 5.9 6.7 5.2 4.3 3.9 4.8 4.5 6.3 2.6 4.3 3.8 4.4 3.1 5.7 4.5 a. Construct comparative boxplots for the yields of the two catalysts and explain the role the whisker plays in data analysis. b. Interpret what the box plot for catalyst B, communicate in real life? mar c. In your own words, give a simple explanation on why statisticians think the sample variance is biased estimator of the population variance and how it could be corrected.
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 certain reaction was run several times using each of the two catalysts, A and B. The catalysts were supposed to control the yield of an undesirable side product.
Results, in units of percentage yield, for 24 runs of catalyst A and 20 runs of catalyst B are as follows:
Catalyst A Catalyst B
4.4 3.4 2.6 3.8 3.4 1.1 2.9 5.5
4.9 4.6 5.2 4.7 6.4 5.0 5.8 2.5
4.1 2.6 6.7 4.1 3.7 3.8 3.1 1.6
3.6 2.9 2.6 4.0 3.5 5.9 6.7 5.2
4.3 3.9 4.8 4.5 6.3 2.6 4.3 3.8
4.4 3.1 5.7 4.5
a. Construct comparative boxplots for the yields of the two catalysts and explain the role the whisker plays in data analysis.
b. Interpret what the box plot for catalyst B, communicate in real life? mar
c. In your own words, give a simple explanation on why statisticians think the sample variance is biased estimator of the population variance and how it could be corrected.
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