Neighborhood 3 1 4 With campaign Without campaign 4.0 3.2 2.5 5.0 2.8 4.0 3.8 4.4 4.3 4.0 Is the amount of food waste per household in the neighborhoods targeted by the campaign lower, on average, than in those not targeted by the campaign? Use a = 0.05.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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Drop-off points (points de collecte in French), where residents can dispose of their organic waste
for composting, were established in each of the five targeted neighborhoods of PROBLEM 1.
Camille wants to see whether or not there exists a relationship between the average weekly amount
of non-disposed food waste per household and the availability of drop-off points in the
neighborhood, expressed as the number of households per drop-off point (considered fixed). Her
data and some of her preliminary calculations are presented below:
Number of
Amount of non-
(x, – x)*
(Y, -Y)
(x; - x)(Y, – Y)
households per
drop-off point
disposed food waste per
household (kg/week)
Yi
Xi
387.5
4.0
7656.25
0.25
43.75
337.5
3.2
1406.25
0.09
-11.25
187.5
2.5
12656.25
1.00
112.50
412.5
5.0
12656.25
2.25
168.75
175.0
2.8
15625
0.49
87.50
E; = 1500
Σ 17.5
E; = 50000
Σ -4.08
Ej = 401.25
2) Camille also calculated the slope of the fitted regression line: estimated slope = 0.008. Test
whether or not the availability of drop-off points in the neighborhood has a linear effect on the
amount of non-disposed food waste per household. Use a =
: 0.10.
Transcribed Image Text:Drop-off points (points de collecte in French), where residents can dispose of their organic waste for composting, were established in each of the five targeted neighborhoods of PROBLEM 1. Camille wants to see whether or not there exists a relationship between the average weekly amount of non-disposed food waste per household and the availability of drop-off points in the neighborhood, expressed as the number of households per drop-off point (considered fixed). Her data and some of her preliminary calculations are presented below: Number of Amount of non- (x, – x)* (Y, -Y) (x; - x)(Y, – Y) households per drop-off point disposed food waste per household (kg/week) Yi Xi 387.5 4.0 7656.25 0.25 43.75 337.5 3.2 1406.25 0.09 -11.25 187.5 2.5 12656.25 1.00 112.50 412.5 5.0 12656.25 2.25 168.75 175.0 2.8 15625 0.49 87.50 E; = 1500 Σ 17.5 E; = 50000 Σ -4.08 Ej = 401.25 2) Camille also calculated the slope of the fitted regression line: estimated slope = 0.008. Test whether or not the availability of drop-off points in the neighborhood has a linear effect on the amount of non-disposed food waste per household. Use a = : 0.10.
Camille for her part wants to assess the impact of an awareness campaign aimed at reducing
the amount of household food waste. The campaign is taking place in a subset of
neighborhoods of Ville de Montréal. Camille's objective is to compare the average amount of
food waste produced in those neighborhoods, with that in neighborhoods not targeted by the
campaign. Therefore, she randomly chooses five neighborhoods targeted by the campaign and
five neighborhoods where the campaign does not take place. In each of the 10 neighborhoods,
she monitors the weekly amount of food waste (kg) for each of a number of households, and
calculates amounts on a per household basis; see below.
Neighborhood
1
2
3
4
5
With campaign
Without campaign
4.0
3.2
2.5
5.0
2.8
4.0
3.8
4.4
4.3
4.0
Is the amount of food waste per household in the neighborhoods targeted by the campaign
lower, on average, than in those not targeted by the campaign? Use a = 0.05.
Transcribed Image Text:Camille for her part wants to assess the impact of an awareness campaign aimed at reducing the amount of household food waste. The campaign is taking place in a subset of neighborhoods of Ville de Montréal. Camille's objective is to compare the average amount of food waste produced in those neighborhoods, with that in neighborhoods not targeted by the campaign. Therefore, she randomly chooses five neighborhoods targeted by the campaign and five neighborhoods where the campaign does not take place. In each of the 10 neighborhoods, she monitors the weekly amount of food waste (kg) for each of a number of households, and calculates amounts on a per household basis; see below. Neighborhood 1 2 3 4 5 With campaign Without campaign 4.0 3.2 2.5 5.0 2.8 4.0 3.8 4.4 4.3 4.0 Is the amount of food waste per household in the neighborhoods targeted by the campaign lower, on average, than in those not targeted by the campaign? Use a = 0.05.
Expert Solution
Working
With Without D (D-Dbar)^2
4 4 0 0.36
3.2 3.8 -0.6 0
2.5 4.4 -1.9 1.69
5 4.3 0.7 1.69
2.8 4 -1.2 0.36


The mean is given by

\overline{d} = \frac{1}{n}\sum d

\overline{d} =\frac{-3}{5} =-0.6

 

The standard deviation is given by

\sigma =\sqrt{\frac{1}{n-1}\sum (d - \overline{d})^2}

\sigma =\sqrt{\frac{4.1}{4}} =1.0124​​​​​​​

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