In the computer game World of Warcraft, some of the strikes are critical strikes

Question

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 211 critical strikes out of 746 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. Your Answer: Answer

Explanation / Answer

We can used one sample proportion z test.

Using minitab.

The command for one sample proportion z test in minitab is

Stat>>>Basic statistics>>>1-proportion...

Then click on summarized data

number of events = x = 211

Number of trials = n = 746

then click on option

Level of confidence in percentage = c = ( 1- lpha)*100 = = (1 -0.05)*100 = 99.0

so put "Confidence level " = 99.0

Alternative = not equal

then click on "Use test and interval based on normal approximation"

Then click on OK and again click on OK

So we get the following output

MTB > POne 746 211;
SUBC>   Confidence 99;
SUBC>   UseZ.

Test and CI for One Proportion

Sample    X    N    Sample p         99% CI
1         211 746 0.282842 (0.240367, 0.325316)

Using the normal approximation.

Lower limit for 99% confidence interval for proportion of strikes that are critical strikes = 0.240

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