A plant physiologist studying a small beach-dwelling plant called the Great Lakes sea rocket, Cakile edentula, investigated whether the plants grew faster in competition with non-kin plants than when in competition with seedlings that are close relatives. She established a direct study of kin recognition by growing sets of four seeds in one container. When the seedlings reached a phase of vigorous root growth, about 8 weeks after planting, she carefully removed the soil and weighed the root masses. Plants grouped with siblings had the following root weight statistics:- Sample size (n) = 24- Mean root weight (X) = 6.25 g- Standard deviation (s) = 0.47 gPlants grouped with unrelated seedlings had the following root weight statistics:- Sample size (n) = 20- Mean root weight (X) = 7.22 g- Standard deviation (s) = 0.55 gThis study raises the question: Are the plants grown in competition with unrelated individuals allocating significantly more resources to root growth than those growing among relatives?

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Description: A plant physiologist studying a small beach-dwelling plant called the Great Lakes sea rocket, Cakile edentula, investigated whether the plants grew faster in competition with non-kin plants than when in competition with seedlings that are close rela

Answered: Plants grouped with siblings had the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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A plant physiologist studying a small beach-dwelling plant called the Great Lakes sea rocket, Cakile edentula, investigated whether the plants grew faster in competition with non-kin plants than when in competition with seedlings that are close relatives. She established a direct study of kin recognition by growing sets of four seeds in one container. When the seedlings reached a phase of vigorous root growth, about 8 weeks after planting, she carefully removed the soil and weighed the root masses.

Plants grouped with siblings had the following root weight statistics:
- Sample size (n) = 24
- Mean root weight (X) = 6.25 g
- Standard deviation (s) = 0.47 g

Plants grouped with unrelated seedlings had the following root weight statistics:
- Sample size (n) = 20
- Mean root weight (X) = 7.22 g
- Standard deviation (s) = 0.55 g

This study raises the question: Are the plants grown in competition with unrelated individuals allocating significantly more resources to root growth than those growing among relatives?

Expert Solution

Step 1

Let $μ_{1}$ denotes the mean root weight of plant grouped with siblings, and $μ_{2}$ denotes the mean root weight of plant grouped with unrelated seedlings. The claim of the test is that the plants grown in competition with unrelated individuals allocating significantly more resources to root growth than those growing among relatives. The hypothesis is,

Null hypothesis:

$H_{0} : μ_{1} - μ_{2} \geq 0$

Alternative hypothesis:

$H_{1} : μ_{1} - μ_{2} < 0$

The pooled variance is,

$\begin{array}{rcl} s_{p}^{2} & = & \frac{(n_{1} - 1) s_{1}^{2} + (n_{2} - 1) s_{2}^{2}}{n_{1} + n_{2} - 2} \\ = & \frac{(24 - 1) 0 . 47^{2} + (20 - 1) 0 . 55^{2}}{24 + 20 - 2} \\ = & 0.2578 \end{array}$

The pooled variance is 0.2578.

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