Question

Give the null and alternative hypotheses in symbolic form that would be used in a hypothesis test of the following claim: "At most 59% of eligible voters actually voted in the last presidential election.

a) H₀: p ≤ 0.59 and Hₐ: p > 0.59
b) H₀: p = 0.59 and Hₐ: p ≠ 0.59
c) H₀: p ≥ 0.59 and Hₐ: p < 0.59
d) H₀: p > 0.59 and Hₐ: p ≤ 0.59

Answer 1

The null and alternative hypotheses in this hypothesis test are H₀: p ≤ 0.59 and Hₐ: p > 0.59.

Step-by-step explanation:

The null and alternative hypotheses in symbolic form that would be used in a hypothesis test of the claim 'At most 59% of eligible voters actually voted in the last presidential election' would be:

a) H₀: p ≤ 0.59 and Hₐ: p > 0.59

Option a) is the correct answer because the claim states 'at most 59%', which implies that the proportion of eligible voters who actually voted is less than or equal to 0.59. Therefore, the null hypothesis (H₀) states that the true proportion is less than or equal to 0.59, while the alternative hypothesis (Hₐ) states that the true proportion is greater than 0.59.