Alan is a frequent flyer for his company. He thinks he gets security-screened more than other passengers. Assume security randomly screens 10% of all people (thus, he should be screened 10% of the time). In the past few years, he has been (randomly?) selected 14 out of 100 times.

What is the null hypothesis (H0) for this test?

Question

Alan is a frequent flyer for his company. He thinks he gets security-screened more than other passengers. Assume security randomly screens 10% of all people (thus, he should be screened 10% of the time). In the past few years, he has been (randomly?) selected 14 out of 100 times.

What is the null hypothesis (H0) for this test?

BlackTom AI · Accepted Answer

The task asks for the null hypothesis (H0) in a test about how often Alan is screened when the screening rate in the population is 10%.

Option review and conceptual checks:
- Since we are dealing with a proportion (the probability of being screened), the parameter of interest is a population proportion, commonly denoted p. The null hypothesis would specify that this proportion equals the claimed rate, here 0.10. 
- A natural alternative would be Ha: p ≠ 0.10 (a two-sided test) unless the problem states a directional alternative (e.g., p > 0.10 or p < 0.10). 
- It is helpful to convert the observed data to an estimate: 14 out of 100 trials gives phat = 0.14. Under H0, the sampling distribution of phat (or the binomial count) is centered at p0 = 0.10, and a standard z or binomial test could be used to assess significance. 
- About the notation: in some contexts people write the null as 𝜇 = 0.10 when 𝜇 is used to denote a mean or a parameter, but for a proportion the standard and clearer notation is p = 0.10. If you see μ used in a multiple-choice item, check whether the course materials treat μ as the population proportion; otherwise the precise statement should be p = 0.10. 
- Given the lack of listed options in the prompt, we can articulate the correct form: H0: p = 0.10. The corresponding Ha would typically be Ha: p ≠ 0.10 (for a two-sided test) unless a specific direction is indicated. 
- Why the null makes sense here: the null anchors the assumption that Alan’s probability of being screened matches the baseline rate (10%), so deviations in observed data are evaluated against this benchmark. 
- Why other potential phrasings would be less appropriate: using a mean μ without clarifying it as a proportion can be ambiguous; claiming H0 is about a difference from 0.10 without naming the parameter as a proportion obscures the model (binomial/normal for phat) and can confuse test statistics. 
- In summary, the clean and conventional null for this test is that the population screening proportion equals 0.10, i.e., H0: p = 0.10 (with the typical alternative Ha: p ≠ 0.10 unless a direction is specified).

stat_400_120258_253926 PA12-3

查看解析

登录即可查看完整答案

类似问题

According to the Food and Nutrition Board of the National Academy of Sciences, the recommended daily allowance (RDA) of calcium for adults is 800 milligrams. We want to see if less than 50% of persons with an income below the poverty level achieve the RDA of 800 mg.

更多留学生实用工具

考试浏览器助手

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