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For n=58 and X=31, find the exact proportions ^p and ^q. ​

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Answer: To find the exact proportions ^p and ^q, we need to use the formulas for sample proportions:

^p = X / n

^q = (n - X) / n

where:

^p = proportion of successes (in this case, the proportion of successes is represented by X)

^q = proportion of failures (1 - ^p)

X = number of successes (in this case, X = 31)

n = total number of trials (in this case, n = 58)

Let's calculate ^p and ^q:

^p = X / n = 31 / 58 ≈ 0.5345 (rounded to four decimal places)

^q = (n - X) / n = (58 - 31) / 58 = 27 / 58 ≈ 0.4655 (rounded to four decimal places)

So, the exact proportions are approximately ^p = 0.5345 and ^q = 0.4655.

User Imapler
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