Question

ANOVA test questions

A) There are five basic assumptions that must be fulfilled in order to perform a one-way ANOVA test. What are they?

Write one assumption. (from the following)

Each population from which a sample is taken is assumed to be uniform.

Each sample is assumed to be uniform.    

Each population from which a sample is taken is assumed to be normal.

Each sample is assumed to be normal.

B) There are five basic assumptions that must be fulfilled in order to perform a one-way ANOVA test. What are they?

Write one assumption. (from the following)

All samples are randomly selected and independent.

All samples are independent.    

All populations are independent.

All samples are randomly selected.

C) State the null hypothesis for a one-way ANOVA test if there are four groups.(from the following)

H₀: none of the group means are equal.

H₀: Only two of the group means μ₁, μ₂, μ₃, μ₄ are equal.    

H₀: At least two of the group means μ₁, μ₂, μ₃, μ₄ are not equal.

H₀: μ₁ = μ₂ = μ₃ = μ₄H₀: μ₁ = μ₂ = μ₃ = μ₄ = 0

D) When do you use an ANOVA test? (from the following)

when you want to test if the variances of at most four populations are equal

when you want to test if the standard deviations of less than four populations are equal    

when you want to test if the means of three or more populations are equalwhen you want to test if the variances of three or more populations are equal

when you want to test if the means of two or more populations are equal

Answer 1

We know that, while doing ANOVA we make several assumptions two of which are, each population is assumed to be normal, and all samples are randomly selected and independent.

A) One assumpton from the given options is:

  Each population from which a sample is taken is assumed to be normal.

B)  One assumpton from the given options is:

  All samples are randomly selected and independent.

C) While doing ANOVA, we test the claim that all the sample means are equal. Therefore, the null hypothesis is:

  H0: μ1 = μ2 = μ3 = μ4

D) We use ANOVA when:

  when you want to test if the means of two or more populations are equal.