In order to increase revenue, many video game publishers sell downloadable conte

Question

In order to increase revenue, many video game publishers sell downloadable content (DLC) separately from the main game. Such content could include additional costumes for the playable characters, additional online game modes, special weapons, etc. A recent industry survey polled 919 game players ages 20 to 30 asking them how important DLC was to their enjoyment of a game. In that sample, 513 people reported that DLC was "very important" to them. Calculate the lower bound of a 90% confidence interval for the true proportion of game players in this age group who believe that DLC is "very important." Take all calculations to three decimal places and report your answer to three decimal places.

Explanation / Answer

Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
No. of success(x)=513
Sample Size(n)=919
Sample proportion = x/n =0.558
Confidence Interval = [ 0.558 ±Z a/2 ( Sqrt ( 0.558*0.442) /919)]
= [ 0.558 - 1.645* Sqrt(0) , 0.558 + 1.65* Sqrt(0) ]
= [ 0.531,0.585]
Interpretations:
1) We are 90% sure that the interval [0.531 , 0.585 ] contains the true population proportion
2) If a large number of samples are collected, and a confidence interval is created
for each sample, 90% of these intervals will contains the true population proportion  

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