MAE108S22p6 (1)
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School
University of California, San Diego *
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Course
108
Subject
Aerospace Engineering
Date
Dec 6, 2023
Type
Pages
2
Uploaded by HighnessSandpiper3218
MAE 108: Probability and Statistical Methods for Mechanical
Engineering
Homework 6 (last one!), Due 1 June 2022 to Gradescope by
11:59pm
1. Related to problem 6.8. The daily dissolved oxygen concentration (DO)
for a location downstream from an industrial plant has been recorded for
the past 10 consecutive days as tabulated in problem 6.8.
You may read about DO at the EPA website: https://www.epa.gov/national-
aquatic-resource-surveys/indicators-dissolved-oxygen
(a) Estimate the sample mean and standard deviation from the data pro-
vided in problem 6.8.
(b) Suppose the minimum mean concentration of DO required by the En-
vironmental Protection Agency is 2.0 mg/l. Perform a hypothesis test
to determine whether the stream quality satisfies the EPA standard
at the significance level of 3%.
(c) You are asked to report the value of DO concentration that the true
mean exceeds with 97% confidence.
Find the one-sided 97% confi-
dence interval on the true mean DO concentration to determine this
value.
2. Problem 8.1 and Matlab regress
(a) Do problem 8.1 following the formulas given in chapter 8, (8.3) and
(8.4).
First determine the stress,
τ
=
x/
area, and the strain,
ϵ
=
y/
length, from the (
x, y
) data provided.
(b) Check your answer to 8.1(b) using Matlab (or whatever language you
prefer) by defining the column vector of stress as B=[1,2,3,4,5,6]’/0.1;
and strain as A=[.009,.020,.028,.041,.052,.063]’/10;, and using the
Matlab command regress(B,A);
(c) Check your answer to 8.1(a) for regression with an intercept by using
the Matlab command regress(B,[ones(length(A),1) A]);
3. Problem 8.2 and Matlab mean, var, regress, and corrcoef
Use the data from problem 8.2 to
(a) Plot the stopping distance versus the speed of travel.
(b) Find the sample mean, variance and standard deviation of both the
stopping distance and the speed of travel using the Matlab commands
mean, var, and std.
Next assume that the stopping distance is a linear function of the
speed so that
E
(
Y
;
x
) =
α
+
βx
(c) Estimate the regression coefficients,
α
and
β
using Matlab regress (re-
gression with an intercept). Plot the regression line with an intercept
on the scatter plot from part (a).
(d) Estimate the regression coefficient without an intercept. Plot this line
on the scatter plot from part (a).
(e) Estimate the correlation coefficient between
Y
and
X
using (8.10).
(f) Use Matlab corrcoef(x,y) to check your answer from (f) for the cor-
relation coefficient.
4. Problem 8.4a,b,c,d,e
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