Question 3 Stu is undertaking a PhD that involves studying the geometric abilities and tendencies of people in the general population. In order to strengthen his PhD research, Stu's supervisor told him that he needed to collect and analyse some real data. Stu therefore selected a random sample of 26 people and asked each person to draw a rectangle on an A4 piece of paper. For each person, Stu recorded the width (X) and the length (Y) of the rectangle, both measured in centimetres. For each person, he also calculated and recorded the quantity A = X x Y. Some sample statistics for the variables X, Y and A are displayed in the table below. Variable X Y A A. Sum of Sample Values Sum of Squared Sample Values Σ, X = 296.4 26 26 X²=3453.3 C. 26 Σ ²₁Y₁ = 293.8 =1 26 Ai = 3408.6 26 Test whether the population mean area of rectangles drawn on an A4 piece of paper is greater than 120.5 centimetres². Clearly state your hypotheses and use a significance level of a = 10%. B. Y² = 3500.92 26 Σ?, A = 493799.815 Test whether the population correlation coefficient between the width and the length of rectangles drawn on an A4 piece of paper is greater than 0. Clearly state your hypotheses and use a significance level of a = 1%. Using the sample data he collected, Stu decides to fit a regression model that can be used to predict the length of a
Question 3 Stu is undertaking a PhD that involves studying the geometric abilities and tendencies of people in the general population. In order to strengthen his PhD research, Stu's supervisor told him that he needed to collect and analyse some real data. Stu therefore selected a random sample of 26 people and asked each person to draw a rectangle on an A4 piece of paper. For each person, Stu recorded the width (X) and the length (Y) of the rectangle, both measured in centimetres. For each person, he also calculated and recorded the quantity A = X x Y. Some sample statistics for the variables X, Y and A are displayed in the table below. Variable X Y A A. Sum of Sample Values Sum of Squared Sample Values Σ, X = 296.4 26 26 X²=3453.3 C. 26 Σ ²₁Y₁ = 293.8 =1 26 Ai = 3408.6 26 Test whether the population mean area of rectangles drawn on an A4 piece of paper is greater than 120.5 centimetres². Clearly state your hypotheses and use a significance level of a = 10%. B. Y² = 3500.92 26 Σ?, A = 493799.815 Test whether the population correlation coefficient between the width and the length of rectangles drawn on an A4 piece of paper is greater than 0. Clearly state your hypotheses and use a significance level of a = 1%. Using the sample data he collected, Stu decides to fit a regression model that can be used to predict the length of a
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Question 3
Stu is undertaking a PhD that involves studying the geometric abilities
and tendencies of people in the general population. In order to
strengthen his PhD research, Stu's supervisor told him that he needed to
collect and analyse some real data. Stu therefore selected a random
sample of 26 people and asked each person to draw a rectangle on an A4
piece of paper. For each person, Stu recorded the width (X) and the
length (Y) of the rectangle, both measured in centimetres. For each
person, he also calculated and recorded the quantity A = X x Y.
Some sample statistics for the variables X, Y and A are displayed in the
table below.
Variable
X
A.
Y
A
Sum of Sample Values Sum of Squared Sample Values
Σ, X, = 296.4
26
Li± X? = 3453.3
26
₁Y² = 3500.92
D.
26
ΣΥ
= 293.8
Σ?%, A; = 3408.6
Σ?, A? =
Test whether the population mean area of rectangles
drawn on an A4 piece of paper is greater than 120.5 centimetres².
Clearly state your hypotheses and use a significance level of
a = 10%.
B.
= 493799.815
Test whether the population correlation coefficient
between the width and the length of rectangles drawn on an A4
piece of paper is greater than 0. Clearly state your hypotheses and
use a significance level of a = 1%.
C.
Using the sample data he collected, Stu decides to fit a
regression model that can be used to predict the length of a
rectangle drawn on an A4 piece of paper from the width of the
rectangle. Calculate the estimates and 3₁.
Using the model fitted in part C, calculate a 99%
prediction interval for the length of a rectangle drawn by someone
on an A4 piece of paper if the width of the rectangle was 11.7
centimetres.
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