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

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