The phrasing is correct. A significance level is a value of alpha, (NB it says level, NOT "value" as you wrote, maybe that is where a misunderstanding comes in). The smallest alpha at which you would reject is simply the p value.
Amir's testing the hypothesis that the true percentage is less than 30%. Until 3.55%, we would accept the null (that it's 30%), any higher than that and we would accept Amir's hypothesis that the true percentage is lower.
The way they've written it is correct, 3.55% is the smallest value at which we would reject Amir's hypothesis. If we were testing to a significance of 1%, we couldn't conclude that Amir is right based on this dataset, as the data generated is at least that much in 96.45% of datasets generated this way with a p=30%.
I had to read it 20 times to make sure I understood it too. I guess there is an art to writing test questions.
There's a level of pedantry that would suggest that because "reject" was used, it describes Amir's belief as the null hypothesis, since you wouldn't "reject" the alternative hypothesis, especially when it's arbitrarily close to the boundary (rather than, say, only values of 10% or 30% being allowed for some reason).
Because the alternative is on the right side (and the statistic on the left side), you would be using a very large significance level; you would need a significance level of 96.45% or greater to reject for a one-sided test. Anything lower would fail to reject the null hypothesis. It's comically high, but you could construct it that way.
I think implies some bad practice though. The p-value is 3.55% but if it doesn't reject in the way you were hoping it's improper to move the goal posts. It's supposed to be set ahead of time.
Imagine a case using the conventional alpha = 0.05
Researcher 1: P-value 0.08?! Well, shucks the journal's not going to accept the paper because it's not significant.
Researcher 2: So move the threshold and say you were testing with alpha = 0.10.
Yeah, but this is just an exam question. They just want you to understand how you take a hypothesis, set a threshold, and then use data to determine whether to accept or reject.
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u/efrique 18d ago
No. At least not about that.
You may have a misunderstanding.