Question

A comparison between species: Biologists wish to compare the prevalence of a genetic mutation across two species of Neema Toads. In a sample of 6 Neema Toads of Species I, 0.7% had the mutation while in a sample of 13 Neema Toads of Species II, 2% showed the mutation. Is there significant evidence to suggest a difference in the prevalence of the mutation across the two species? Conduct a hypothesis test at a significance level of α=0.05α=0.05.

a) The hypotheses for this test are:

- H₀: pᵢᵢ = 0.007
Ha: pᵢᵢ ≠ 0.007

- H₀: pᵢ - pᵢᵢ = 0
Ha: pI - pᵢᵢ < 0

- H₀: pᵢ - pᵢᵢ = 0
Ha: pᵢ - pᵢᵢ ≠ 0

- H₀: pᵢ - pᵢᵢ = 0
Ha: pᵢ - pᵢᵢ > 0

Answer 1

In hypothesis testing for comparing two proportions, if the p-value is less than the chosen significance level, the null hypothesis is rejected, indicating a significant difference. The specific decision depends on both the p-value obtained from the test and the predetermined significance level, α.

Step-by-step explanation:

To determine whether there is a significant difference in the prevalence of a genetic mutation across two species of Neema Toads, a hypothesis test can be utilized. The appropriate hypotheses for a two-sample test of proportions are H₀: pₗ - pₘ = 0 and Ha: pₗ - pₘ ≠ 0. Here, pₗ is the proportion of species I with the mutation and pₘ is the proportion of species II with the mutation.

Using the calculator function 2-PropZTest, we find a p-value. If the p-value is less than the significance level α (alpha), we reject the null hypothesis, suggesting a significant difference between the two proportions. For example, if the p-value = 0.0417 and α = 0.05, we would reject H₀ and conclude there is a significant difference. However, if using a more stringent level of α = 0.01, the p-value is greater than α, leading us to not reject H₀ and conclude there is insufficient evidence of a difference.