4) Apply the sample size determination formula to solve the followingapplication:An investor is considering funding a new video game. He wants to know theworldwide percentage of people who play video games, so a survey is beingplanned. How many people must be surveyed to be 90% confident that theestimated percentage is within three percentage points of the truepopulation percentage.a) Assume that about 16% of people play video games.b) Assume that nothing is known about the worldwide percentage of peoplewho play video games.c) Given that the required sample size is relatively small, could you simplysurvey the people that you know? How large a random sample do we need for the sample to bereasonable representative of the population? Most people think that we need alarge percentage of the population, but it turns out that all that matters are thenumber of individuals in the sample. A random sample of 100 students in a collegerepresents the student body just about as well as a random sample of 100 votersrepresents the entire electorate of the United States. How can it be that only thesize of the sample, and not the population, matters?Imagine you a cooking soup. If you are cooking for a banquet rather than just for afew people, your pot will be bigger, but do you need a bigger spoon to decide howthe soup taste? Of course not. The same size spoonful is probably enough to decideabout the entire pot, no matter how large the pot. The fraction of the populationthat you've sampled doesn't matter. It's the sample, the number of individuals inthe sample, that is important.In this activity you will start with the Margin of Error formula and use algebraicmanipulations to find a formula for the sample size required to estimate apopulation proportion.Determining Sample SizepqE = z,(solve for n by algebra)(z)² êâqn =E?ALWAYS LEARNINGCopyright e 2014, 2012, 2010 Pearson Education, Inc.PEARSON Section 7.2-271) Show your work step by step2) Explain the meaning of each variable in the formula.3) What would happen if p-hat is unknown? How would you need to changethe formula?4) Apply the sample size determination formula to solve the followingapplication:An investor is considering funding a new video game. He wants to know theworldwide percentage of people who play video games, so a survey is beingplanned. How many people must be surveyed to be 90% confident that theestimated percentage is within three percentage points of the truenonulation nercentage

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formula for the sample size needed to estimate a population proportion is