Statistics - Proportions to make Inferences

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What is a proportion?

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A proportion is a mathematical equation that states that two ratios are equal. It is often used to compare parts of a whole.

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How do you calculate a proportion from a sample?

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To calculate a proportion from a sample, divide the number of favorable outcomes by the total number of outcomes in the sample.

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CCSS.HSS.IC.B.4

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What is the purpose of using a sample in statistics?

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A sample is used in statistics to make inferences about a larger population without having to collect data from every individual in that population.

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If 12 out of 60 dogs are puppies, what is the proportion of puppies?

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The proportion of puppies is 12/60, which simplifies to 1/5 or 0.2.

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CCSS.6.RP.A.1

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How can you estimate the number of puppies in a larger population using a sample?

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To estimate the number of puppies in a larger population, multiply the proportion of puppies in the sample by the total number of individuals in the population.

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CCSS.7.SP.A.2

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What is the formula to estimate a population based on a sample?

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Estimated population = (Number of favorable outcomes in sample / Total outcomes in sample) x Total population.

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CCSS.7.SP.A.2

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In a sample of 50 elk, if 8 are infected, what is the infection rate?

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The infection rate is 8/50, which simplifies to 0.16 or 16%.

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How do you apply the infection rate to estimate the number of infected elk in a population of 4,500?

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Multiply the infection rate (0.16) by the total population (4,500) to estimate the number of infected elk: 0.16 x 4,500 = 720 elk.

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CCSS.7.SP.A.2

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What is a random sample?

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A random sample is a subset of individuals chosen from a larger population, where each individual has an equal chance of being selected.

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Why is it important to use random sampling in statistics?

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Random sampling helps to eliminate bias and ensures that the sample is representative of the population, leading to more accurate inferences.

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