In: Statistics and Probability
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 261 critical strikes out of 721 attacks. What is the
lower bound for the 99% confidence interval for the proportion of
strikes that are critical strikes.
Round to three decimal places (for example: 0.419). Write only a
number as your answer.
Solution :
Given that,
n = 721
x = 261
= x / n =261 /721 = 0.362
1 - = 1 - 0.362 = 0.638
At 99% confidence level the z is ,
= 1 - 99% = 1 - 0.99 = 0.01
/ 2 = 0.01 / 2 = 0.005
Z/2 = Z0.005 = 2.576
Margin of error = E = Z / 2 * (( * (1 - )) / n)
= 2.576 * (((0.362 * 0.638) / 721) = 0.046
A 99 % confidence interval for population proportion p is ,
- E < P < + E
0.362 - 0.046 < p < 0.362 + 0.046
0.316< p <0.408
The 99% confidence interval for the population proportion p is : ( 0.316 , 0.408)