Answer to Question #225783 in Statistics and Probability for Muqadas

Question

1Consider the following data set, in which shrinkage is measured once again at low injection velocity and high injection velocity. However, this time the mold temperature is raised to a high level and held constant.
Shrinkage values at low injection velocity:
76.20 76.09 75.98 76.15 76.17 75.94 76.12 76.18 76.25 75.82 Shrinkage values at high injection velocity:
93.25 93.19 92.87 93.29 93.37 92.98 93.47 93.75 93.89 91.62
(a)Check the distributions of the data.
(b)Whether distribution is (i) leptokurtic (ii) meso-kurtic (iii) platy-kurtic?

Answer 1

Using R

(a) The output from the shapiro.test( ) function suggests that the shrinkage values at low injection velocity dataset is normally distributed (p = 0.2675 > 0.05) while the results for shrinkage values at high injection velocity suggest that these dataset are not normally distributed (p ≤ 0.05).

(b) Be sure you’ve installed the e1071 package and loaded it with the library( ) function. You can run the following lines of code to test for kurtosis.

If kurtosis is near zero then the distribution is “mesokurtic,” or is consistent with a bell-shaped curve without a really sharp peak or a flat-topped peak. If the value is a relatively large, positive number then the data are more pointy in the middle than a regular, bell-shaped distribution. Such a distribution is referred to as being “leptokurtic.” If the value is negative then the distribution is relatively flat-topped.

As we can see here the kurtosis value for shrinkage values at low injection velocity is negative.

The shrinkage values at low injection velocity distribution is referred to as being “platykurtic”.

The kurtosis value for shrinkage values at high injection velocity is positive.

The shrinkage values at high injection velocity distribution is referred to as being “leptokurtic”.