Question

Independent random samples were selected from two binomial populations, with sample sizes and the number of successes given below. Population 1 2 Sample Size 500 500 Number of Successes 118 146 State the null and alternative hypotheses to test for a difference in the two population proportions.

Answer 1

The null and alternative hypotheses for the test are:

H₀: p₁ - p₂ = 0 vs. Hₐ: ₁ - p₂ ≠ 0.

Explanation:

Te information provided is:

Population: 1 2

Sample size: 500 500

Number of successes: 118 146

In this case we need to test whether there is any difference between the two population proportions.

The test for the significant difference between the two population proportions can be performed using the z-distribution.

The hypothesis for this test can be defined as:

H₀: There is no difference between the two population proportions, i.e. p₁ - p₂ = 0.

Hₐ: There is a difference between the two population proportions, i.e. p₁ - p₂ ≠ 0.

Thus, the null and alternative hypotheses for the test are:

H₀: p₁ - p₂ = 0 vs. Hₐ: ₁ - p₂ ≠ 0.