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 944 game players ages 20 to 30 asking them how important DLC was to their enjoyment of a game. In that sample, 789 people reported that DLC was "very important" to them.

Suppose that the company conducting the survey wants to test the hypothesis that the true population proportion of game players who believe DLC is "very important" is 0.5. Calculate the value of the test statistic to two decimal places.

Explanation / Answer

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.5
Ha:   p   =/=   0.5

As we see, the hypothesized po =   0.5      

Getting the point estimate of p, p^,          
          
p^ = x / n =    0.835805085      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.016273614      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    20.63494239 = 20.63 [ANSWER]  
          

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