4) Apply the sample size determination formula to solve the following application: An investor is considering funding a new video game. He wants to know the worldwide percentage of people who play video games, so a survey is being planned. How many people must be surveyed to be 90% confident that the estimated percentage is within three percentage points of the true population percentage. a) Assume that about 16% of people play video games. b) Assume that nothing is known about the worldwide percentage of people who play video games. c) Given that the required sample size is relatively small, could you simply survey the people that you know?

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4) Apply the sample size determination formula to solve the following
application:
An investor is considering funding a new video game. He wants to know the
worldwide percentage of people who play video games, so a survey is being
planned. How many people must be surveyed to be 90% confident that the
estimated percentage is within three percentage points of the true
population percentage.
a) Assume that about 16% of people play video games.
b) Assume that nothing is known about the worldwide percentage of people
who play video games.
c) Given that the required sample size is relatively small, could you simply
survey the people that you know?
Transcribed Image Text:4) Apply the sample size determination formula to solve the following application: An investor is considering funding a new video game. He wants to know the worldwide percentage of people who play video games, so a survey is being planned. How many people must be surveyed to be 90% confident that the estimated percentage is within three percentage points of the true population percentage. a) Assume that about 16% of people play video games. b) Assume that nothing is known about the worldwide percentage of people who play video games. c) Given that the required sample size is relatively small, could you simply survey the people that you know?
How large a random sample do we need for the sample to be
reasonable representative of the population? Most people think that we need a
large percentage of the population, but it turns out that all that matters are the
number of individuals in the sample. A random sample of 100 students in a college
represents the student body just about as well as a random sample of 100 voters
represents the entire electorate of the United States. How can it be that only the
size of the sample, and not the population, matters?
Imagine you a cooking soup. If you are cooking for a banquet rather than just for a
few people, your pot will be bigger, but do you need a bigger spoon to decide how
the soup taste? Of course not. The same size spoonful is probably enough to decide
about the entire pot, no matter how large the pot. The fraction of the population
that you've sampled doesn't matter. It's the sample, the number of individuals in
the sample, that is important.
In this activity you will start with the Margin of Error formula and use algebraic
manipulations to find a formula for the sample size required to estimate a
population proportion.
Determining Sample Size
pq
E = z,
(solve for n by algebra)
(z)² êâq
n =
E?
ALWAYS LEARNING
Copyright e 2014, 2012, 2010 Pearson Education, Inc.
PEARSON Section 7.2-27
1) Show your work step by step
2) Explain the meaning of each variable in the formula.
3) What would happen if p-hat is unknown? How would you need to change
the formula?
4) Apply the sample size determination formula to solve the following
application:
An investor is considering funding a new video game. He wants to know the
worldwide percentage of people who play video games, so a survey is being
planned. How many people must be surveyed to be 90% confident that the
estimated percentage is within three percentage points of the true
nonulation nercentage
Transcribed Image Text:How large a random sample do we need for the sample to be reasonable representative of the population? Most people think that we need a large percentage of the population, but it turns out that all that matters are the number of individuals in the sample. A random sample of 100 students in a college represents the student body just about as well as a random sample of 100 voters represents the entire electorate of the United States. How can it be that only the size of the sample, and not the population, matters? Imagine you a cooking soup. If you are cooking for a banquet rather than just for a few people, your pot will be bigger, but do you need a bigger spoon to decide how the soup taste? Of course not. The same size spoonful is probably enough to decide about the entire pot, no matter how large the pot. The fraction of the population that you've sampled doesn't matter. It's the sample, the number of individuals in the sample, that is important. In this activity you will start with the Margin of Error formula and use algebraic manipulations to find a formula for the sample size required to estimate a population proportion. Determining Sample Size pq E = z, (solve for n by algebra) (z)² êâq n = E? ALWAYS LEARNING Copyright e 2014, 2012, 2010 Pearson Education, Inc. PEARSON Section 7.2-27 1) Show your work step by step 2) Explain the meaning of each variable in the formula. 3) What would happen if p-hat is unknown? How would you need to change the formula? 4) Apply the sample size determination formula to solve the following application: An investor is considering funding a new video game. He wants to know the worldwide percentage of people who play video games, so a survey is being planned. How many people must be surveyed to be 90% confident that the estimated percentage is within three percentage points of the true nonulation nercentage
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