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I have this data for exam grades in English Literature:

2019: the numbers achieving (A*, A, B, C, D, E) are (1, 5, 4, 7, 2, 0, 0)

2018: the numbers achieving (A*, A, B, C, D, E) are (2, 4, 3, 7, 0, 1, 0)

2017: the numbers achieving (A*, A, B, C, D, E) are (6, 5, 3, 4, 2, 0, 0)

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Suppose someone says, "In 2020, if we have 20 students, the percentage getting A* will be between 10% and 20%", how do I calculate the confidence level of that statement? Alternatively, how do I calculate the 80% confidence interval?

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    $\begingroup$ Such a statement is a prediction, not an estimate, and therefore (a) it needs to be specific, as in "the percentage getting A* will be 15%," and (b) the appropriate interval is called a prediction interval. Prediction intervals are not confidence intervals. Finally, there are many possible good answers: they will vary according to how you model the evolution of data over time. E.g., are you willing to suppose the proportions are changing over time or do you wish to assume they are constant? Answers will also change if you simultaneously want prediction intervals for other grades. $\endgroup$
    – whuber ♦
    Jul 22, 2020 at 18:29
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    $\begingroup$ Thanks, whuber. The proportions are assumed to be theoretically constant over time, and I would like to predict the number getting each grade if there are 20 students this year. What would these predictions be and what would be the 80% prediction interval for each grade? $\endgroup$
    – user810739
    Jul 22, 2020 at 19:31
  • $\begingroup$ It sounds like you need a prediction interval for a Binomial GLM. This has been discussed on CV a few times, at stats.stackexchange.com/questions/26568/… and stats.stackexchange.com/questions/41074, with no answer. A sketch of an answer in a closely related situation appears at stats.stackexchange.com/a/42958. Are these on the right track? $\endgroup$
    – whuber ♦
    Jul 23, 2020 at 14:15

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