Jade works at an insectarium and is conducting a study that investigates the possible effects of three different food types (type 1, 2 and 3) on adult size among three species of butterfly (species A, B and C). For each particular combination of food type and species, Jade randomly selected three butterflies from that species which were raised only on that food type until they reached adult size. For each butterfly, Jade recorded the adult wingspan (Y) in centimetres. Some sample statistics are displayed in the table below. Food Type Sum of Sample Values Sum of Squared Sample Values 1 Σ Υ = 38.7 2_n Yỉ = 168.93 Y₂=217.15 2 Σ1Y2i = 44.1 3 Y3i = 52.2 Y=310.50 Test whether the population variance of butterfly wingspan is the same for butterflies raised on food type 1 and for butterflies raised on food type 2. Clearly state your hypotheses and use a significance level of a = 5% Test whether the population mean wingspan of butterflies raised on food type 2 is greater than the population mean wingspan of butterflies raised on food type 1 by more than 0.2 centimetres. Clearly state your hypotheses and use a significance level of a = 10%- C. A. B Assuming that any required assumptions are satisfied, use a one-way ANOVA with food type as the factor to test whether there is a difference in the population mean wingspan of butterflies between the three food types. Clearly state your hypotheses and use a significance level of a = 1% For the same sample data that Jade collected, some additional sample statistics are displayed in the table below. Species Sum of Sample Values Σ1 YA = 42.3 A B Σi1YBi = 44.1 C Yci = 48.6
Jade works at an insectarium and is conducting a study that investigates the possible effects of three different food types (type 1, 2 and 3) on adult size among three species of butterfly (species A, B and C). For each particular combination of food type and species, Jade randomly selected three butterflies from that species which were raised only on that food type until they reached adult size. For each butterfly, Jade recorded the adult wingspan (Y) in centimetres. Some sample statistics are displayed in the table below. Food Type Sum of Sample Values Sum of Squared Sample Values 1 Σ Υ = 38.7 2_n Yỉ = 168.93 Y₂=217.15 2 Σ1Y2i = 44.1 3 Y3i = 52.2 Y=310.50 Test whether the population variance of butterfly wingspan is the same for butterflies raised on food type 1 and for butterflies raised on food type 2. Clearly state your hypotheses and use a significance level of a = 5% Test whether the population mean wingspan of butterflies raised on food type 2 is greater than the population mean wingspan of butterflies raised on food type 1 by more than 0.2 centimetres. Clearly state your hypotheses and use a significance level of a = 10%- C. A. B Assuming that any required assumptions are satisfied, use a one-way ANOVA with food type as the factor to test whether there is a difference in the population mean wingspan of butterflies between the three food types. Clearly state your hypotheses and use a significance level of a = 1% For the same sample data that Jade collected, some additional sample statistics are displayed in the table below. Species Sum of Sample Values Σ1 YA = 42.3 A B Σi1YBi = 44.1 C Yci = 48.6
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:Calculate the sum of squares for treatment in a one-way
ANOVA with species as the factor.
E.
Jade asked her colleague to perform a two-way ANOVA
on the same sample data with food type and species as the two
factors. Her colleague performed the two-way ANOVA (assuming
any required assumptions were satisfied) but unfortunately
misplaced the results. All that he could remember was that there
was an interaction between food type and species at the 5%
significance level but not at the 2.5% significance level. Calculate
the two values between which the sum of squares for interaction in
this two-way ANOVA must lie.
D.
Transcribed Image Text:Question 5
Jade works at an insectarium and is conducting a study that investigates
the possible effects of three different food types (type 1, 2 and 3) on
adult size among three species of butterfly (species A, B and C). For each
particular combination of food type and species, Jade randomly selected
three butterflies from that species which were raised only on that food
type until they reached adult size. For each butterfly, Jade recorded the
adult wingspan (Y) in centimetres. Some sample statistics are displayed
in the table below.
Food Type Sum of Sample Values Sum of Squared Sample Values
1
Σ Υ = 38.7
Σ= Y = 168.93
2
Σ1Y2i = 44.1
3
₁1Y3i = 52.2
A.
Test whether the population variance of butterfly
wingspan is the same for butterflies raised on food type 1 and for
butterflies raised on food type 2. Clearly state your hypotheses and
use a significance level of a = 5%
Test whether the population mean wingspan of butterflies
raised on food type 2 is greater than the population mean wingspan
of butterflies raised on food type 1 by more than 0.2 centimetres.
Clearly state your hypotheses and use a significance level of
a = 10%.
C.
B
1Y2 = 217.15
ΣY3 = 310.50
i=1
Assuming that any required assumptions are satisfied,
use a one-way ANOVA with food type as the factor to test whether
there is a difference in the population mean wingspan of butterflies
between the three food types. Clearly state your hypotheses and
use a significance level of a =
1%
For the same sample data that Jade collected, some additional sample
statistics are displayed in the table below.
Species Sum of Sample Values
Σ= ΥΑ = 42.3
A
Σi1YBi = 44.1
Yci = 48.6
B
C
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VIEWStep 2: Test the significance that the population variances for food type 1 and food type 2 are same or not
VIEWStep 3: Test the significance that the population mean for food type 2 is greater than that for food type 1
VIEWStep 4: Test whether there is a difference in the population mean wingspan of butterflies
VIEWStep 5: Calculate the sum of squares for treatment for factor species
VIEWStep 6: Calculate the two values between which the sum of squares for interaction must lie in 2-way ANOVA
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