Let X and Y equal the hardness of the hot and cold water, respectively, in a campus building. Hardness is measured in terms of the calcium ion concentration (in ppm). The following data were collected (n = 12 observations of X and m = 10 observations of Y): %3D X: 133.5 137.2 136.3 133.3 137.5 135.4 138.4 137.1 136.5 139.4 137.9 136.8 y: 134.0 134.7 136.0 132.7 134.6 135.2 135.9 135.6 135.8 134.2 (a) Calculate the sample means and the sample variances of these data. (b) Construct a 95% confidence interval for ux- Hy, assuming that the distributions of X and Y are N(µx, o² x) and N(uy, o2 y ), respectively. (c) Construct box plots of the two sets of data on the same graph. (d) Do the means seem to be equal or different?
Let X and Y equal the hardness of the hot and cold water, respectively, in a campus building. Hardness is measured in terms of the calcium ion concentration (in ppm). The following data were collected (n = 12 observations of X and m = 10 observations of Y): %3D X: 133.5 137.2 136.3 133.3 137.5 135.4 138.4 137.1 136.5 139.4 137.9 136.8 y: 134.0 134.7 136.0 132.7 134.6 135.2 135.9 135.6 135.8 134.2 (a) Calculate the sample means and the sample variances of these data. (b) Construct a 95% confidence interval for ux- Hy, assuming that the distributions of X and Y are N(µx, o² x) and N(uy, o2 y ), respectively. (c) Construct box plots of the two sets of data on the same graph. (d) Do the means seem to be equal or different?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Let X and Y equal the hardness of the
hot and cold water, respectively, in a
campus building. Hardness is
measured in terms of the calcium ion
concentration (in ppm). The following
data were collected (n = 12
observations of X and m = 10
observations of Y):
%3D
x:
133.5
137.2
136.3
133.3
137.5
135.4
138.4
137.1
136.5
139.4
137.9
136.8
y:
134.0
134.7
136.0
132.7
134.6
135.2
135.9
135.6
135.8
134.2
(a) Calculate the sample means and
the sample variances of these data.
(b) Construct a 95% confidence
interval for ux - Hy, assuming that the
distributions of X and Y are N(x, o² x)
and N(uy, o? y ), respectively.
(c) Construct box plots of the two
sets of data on the same graph.
(d) Do the means seem to be equal or
different?
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