Question

For this discussion, I chose option two again to determine what the population proportion is for those who own an Xbox One compared to a PlayStation 4 or PC. Suppose I interview 400 people at a gaming convention, say PAX East, and asked them which game system they preferred. After I was done interviewing these people, I concluded that 160 people owned an Xbox One, while the other 240 people owned either the PlayStation 4 or a PC. I have a 95% confidence level of this estimate that a little bit under half of all gamers out there own the Xbox and are happy with this system and will not switch down the line. What is the population proportion for this data set and do you agree in the assumption that the divide between these systems is accurate? I look forward to seeing your answers for this data set.

Answer 1

As the total sample size of the study is taken to be 400 respondent. The division as suggested in the problem is:

Gaming Option	Xbox	Playstation	PC
Owned	160	240

The given data suggest that for the sample population the % of people who owns xbox will be:

% of people owning xbox: 160/400(p) = 0.4 = 40%.

% of people not owning xbox(q)=1-0.4 = 0.6

Now we need to arrive at the population from the sample data which states that around 50% of the people own Xbox & will not switch.

Total population information is missing in the case so we need to find the z score for the 95% confidence interval which will be 1.96.

Now the formula will be = z*(p*q/n)^0.5 = 0.0245

Hence the confidence interval for proportion will be =0.4+0.0245 =0.424495

= 0.4-0.0245 = 0.375505

Hence the population maximum value can go upto 0.424495 which will be 42.44%. Hence te guess which the observer is carrying is not inline will the data output.