ETM501 Exercise I

The following random sample of size n=30 is collected by measuring a certain dimension of a product Y. This dimension is claimed to be normally distributed with mean 50 and variance 1.

49,60 49,12 50,06 49,63 49,45 51,19 49,95 49,61 52,18 49,74 50,61 49,64 50,09 50,35 50,64 48,51 50,73 48,61 50,44 50,58 50,11 51,11 48,73 51,07 49,44 50,55 48,14 50,34 50,50 49,19

1. Compute the descriptive statistics: mean, variance, standard deviation, range, coefficient of variation. 2. Order the data set from the minimum to the maximum. Compute the quartiles and the interquartile range. 3. Draw the histogram, stem-and-leaf diagram and the box plot for the given data. 4. Based on your analysis, do you agree with the claim that Y is distributed as Normal(50,1). Comment on your answer. You are expected to carry out the analysis by manual computations: Afterwards, you can check your analysis with the Minitab output below. Solutions to Questions 1 and 2. Descriptive Statistics: C1 Variable Mean SE Mean StDev Variance CoefVar Minimum Q1 Median C1 49,997 0,163 0,893 0,797 1,79 48,140 49,448 50,075 Variable Q3 Maximum Range IQR C1 50,588 52,180 4,040 1,140 Solution for Question 3.

Stem-and-leaf of C1 N = 30 Leaf Unit = 0,10 1 48 1 4 48 567 8 49 1144 14 49 666679 (6) 50 001334 10 50 555667 4 51 011 1 51 1 52 1

Solution for Question 4. Based on the analysis, the random sample agrees with the normal distribution Normal(50,1). You can further compare the empirical cdf with the Normal cdf.