A population geneticist is studying a population of pea aphids and wants to determine whether the proportion p of aphids that are resistant to a particular insecticide is less than 0.40, the proportion reported in a previous study. Which pair of hypotheses is appropriate for this test?

Question

BlackTom AI · Accepted Answer

Because the researcher’s claim is that the true proportion is lower than 0.40, the alternative hypothesis must be directional and state p < 0.40. In hypothesis testing for a population proportion, the null hypothesis is the status-quo or the statement of equality (or the non-directional complement) and the alternative expresses the claim to be tested. Thus the correct pairing is H0: p = 0.40 and Ha: p < 0.40.

Relevant concepts:
- Null hypothesis (H0) typically includes equality (p = p0) or a non-directional complement (sometimes written H0: p ≥ p0) and represents the assumption tested.
- Alternative hypothesis (Ha) reflects the research claim; here it is one-sided (left-tailed) because the researcher suspects p is smaller.
- This setup leads to a left-tailed test (for example, a one-proportion z-test if sample size assumptions are satisfied).

Step-by-step reasoning:
1. Identify the research claim: “p is less than 0.40.” That directly determines Ha: p < 0.40.
2. Form the null as the complement that includes equality: H0: p = 0.40 (equivalently H0: p ≥ 0.40 in some texts). This ensures the null is a specific value against which sample evidence is compared.
3. Use the left-tailed test framework: if the sample proportion is sufficiently below 0.40 (with a p-value below α), reject H0 in favor of Ha.

Why this answer is correct:
- It places the researcher’s claim in the alternative and sets the null as the baseline equality; this is standard practice for directional hypothesis tests.

Why other plausible options are incorrect:
- H0: p = 0.40 vs Ha: p > 0.40 would test whether p is greater, opposite the claim.
- A two-sided pair (H0: p = 0.40 vs Ha: p ≠ 0.40) tests for any difference, not specifically less than 0.40.
- Writing the null as H0: p < 0.40 is inappropriate because the null generally includes equality and is what we assume unless evidence rejects it.

Therefore, the appropriate hypothesis pair is H0: p = 0.40 vs Ha: p < 0.40, which matches the provided answer.

类似问题

Which of the following is a factor that, by itself, is least likely to promote widespread changes in allele or genotype frequencies in a large population?

In natural populations, most genes are

Which of the following is a factor that does not promote widespread changes in allele or genotype frequencies?

The Greater prairie chicken population in Illinois is a living example of which of these ?

A population that is infinitely large and in which mating is completely random is mostly likely to:

Question at position 21 What is the most important determinant of genetic differences between populations of humans across the world?RaceEthnicityGeographic distanceLocal adaptationClear my selection

Question at position 14 Genetic diversity amongst human populations is best explained by __________.cultural differencespopulation sizeethnicityracial categorizesgeographic distanceClear my selection

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单