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

249

critical strikes out of

588

attacks.

(a) Construct a

99.5%

confidence interval for the proportion of strikes that are critical strikes. Round the answer to at least three decimal places.

b) Construct a

95%

confidence interval for the proportion of strikes that are critical strikes. Round the answer to at least three decimal places.

c) What is the effect of increasing the level of confidence on the width of the interval? (narrower, wider)

Answer 1

Solution :

Given that,

n = 588

x = 249

=x / n = 249 / 588 = 0.423

1 - = 1 - 0.423 = 0.577

(a)

At 99.5% confidence level the z is ,

= 1 - 99.5% = 1 - 0.995 = 0.005

/ 2 = 0.005 / 2 = 0.0025

Z_/2 = Z_0.0025 = 2.81

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 2.81 * (((0.423 * 0.577) / 588)

= 0.057

A 99.5% confidence interval for population proportion p is ,

- E < P < + E

0.423 - 0.057 < p < 0.423 + 0.057

0.366 < p < 0.480

(0.366 , 0.480)

(b)

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.96 * (((0.423 * 0.577) / 588)

= 0.039

A 95% confidence interval for population proportion p is ,

- E < P < + E

0.423 - 0.039 < p < 0.423 + 0.039

0.384 < p < 0.462

(0.384 , 0.462)

(c)

Increasing the level of confidence on the width of the interval is increases .

Wider