Exercise 1: A Different Historical Baseline — Possible Solution
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GIVEN
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45 conversions out of 500 sessions

STEP 1: THE POINT ESTIMATE
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p = 45 / 500 = 0.09 (9%)

STEP 2: THE STANDARD ERROR
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SE = sqrt(p(1-p)/n) = sqrt(0.09 x 0.91 / 500) = sqrt(0.0819/500)
   ~= 0.01280

STEP 3: THE 95% CONFIDENCE INTERVAL
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CI = p +/- 1.96 x SE = 0.09 +/- 1.96(0.01280) = 0.09 +/- 0.02509

  CI = [0.0649, 0.1151] (approximately 6.5% to 11.5%)

WHY THIS WORKS AS AN ANSWER
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The point estimate and its confidence interval are computed using
exactly this chapter's own Steps 1-2 method - treating the historical
count as a sample proportion, computing its standard error, and
building the interval around it - applied to the new baseline figures
rather than the chapter's own original 8% example.