Step 1 :First, we need to calculate the sample proportion (p̂). This is done by dividing the number of critical strikes (238) by the total number of attacks (599).
Step 2 :Next, we calculate the standard error (SE) using the formula \( \sqrt{(p̂*(1-p̂))/n} \), where n is the total number of attacks.
Step 3 :Then, we calculate the confidence interval using the formula \( p̂ ± Z*SE \). Here, Z is the z-score corresponding to our desired confidence level of 98%, which is approximately 2.33.
Step 4 :Substituting the values we have, we get \( p̂ = 0.397 \), \( SE = 0.020 \), \( CI_{lower} = 0.351 \), and \( CI_{upper} = 0.444 \).
Step 5 :Final Answer: A 98% confidence interval for the proportion of strikes that are critical strikes is \( \boxed{0.351}