Question

a group of researchers is studying the effect of different types of light on plant growth. they categorize 70 plants into two categories based on their growth (healthy or unhealthy) and expose them to three different types of light (natural sunlight, led light, fluorescent light). after 4 weeks, they collect the following data:

which option correctly states the null and alternative hypotheses to determine whether the type of light affects plant growth?

• ho: the type of light do not affect the plant growth.

h1: the type of light do affect the plant growth.

• ho: the type of light do affect the plant growth.

h1: the type of light do not affect the plant growth.

• \\(h_0 : \mu_{\text{type of light}} = \mu_{\text{plant growth}}\quad vs.\quad h_1 : \mu_{\text{type of light}} \

eq \mu_{\text{plant growth}}\\)

• \\(h_0 : \mu_{\text{type of light}} \

eq \mu_{\text{plant growth}}\quad vs.\quad h_1 : \mu_{\text{type of light}} = \mu_{\text{plant growth}}\\)

Explanation:

🆕 New Concept Discovered: Chi-Square Test of Independence
Testing if two categorical variables are related.

Step 1: Identify the Variable Types

The study involves two categorical variables:

1. Light Type (Natural Sunlight, LED Light, Fluorescent Light)
2. Plant Growth (Healthy, Unhealthy)

When analyzing the relationship between two categorical variables presented in a contingency table, we use a Chi-Square Test of Independence.

Step 2: Define the Null and Alternative Hypotheses

In a test of independence:

• Null Hypothesis (\(H_0\)): Assumes there is no association or effect. In this context, it means the type of light does not affect (is independent of) plant growth.
• Alternative Hypothesis (\(H_1\)): Assumes there is an association or effect. In this context, it means the type of light does affect (is not independent of) plant growth.

Step 3: Match with the Given Options

• Option 1:

\(H_0\): The type of light do not affect the plant growth.
\(H_1\): The type of light do affect the plant growth.
(This correctly states that the null hypothesis is the status quo of "no effect" and the alternative is "does affect".)

• Option 2: Reverses \(H_0\) and \(H_1\).
• Options 3 & 4: Use population means (\(\mu\)), which are used for quantitative variables, not categorical variables.

Answer:

• \(H_0\): The type of light do not affect the plant growth.

\(H_1\): The type of light do affect the plant growth.