Problem

WoW: In the computer game World of Warcraft, some of the strikes are critical strikes, which do more damage. Assume that the probability of a critical strike is the same for every attack, and that attacks are independent. During a particular fight, a character has 238 critical strikes out of 599 attacks.
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Part 1 of 3
(a) Construct a 98% confidence interval for the proportion of strikes that are critical strikes. Round the answer to at least three decimal places. A 98% confidence interval for the proportion of strikes that are critical strikes is <p<.

Answer

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Answer

Final Answer: A 98% confidence interval for the proportion of strikes that are critical strikes is 0.351<p<0.444.

Steps

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 (p̂(1p̂))/n, where n is the total number of attacks.

Step 3 :Then, we calculate the confidence interval using the formula p̂±ZSE. 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, CIlower=0.351, and CIupper=0.444.

Step 5 :Final Answer: A 98% confidence interval for the proportion of strikes that are critical strikes is \( \boxed{0.351}

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