A market research company conducted a survey to find the level of affluence in a city. They defined the category "affluence" for people earning $100,000 or more annually. Out of 267 persons who replied to their survey, 32 are considered affluent.What is the 95% confidence interval for this population proportion? Answer choices are rounded to the hundredths place.0.08 to 0.340.16 to 0.240.24 to 0.340.08 to 0.16
Question
A market research company conducted a survey to find the level of affluence in a city. They defined the category "affluence" for people earning $100,000 or more annually. Out of 267 persons who replied to their survey, 32 are considered affluent.What is the 95% confidence interval for this population proportion? Answer choices are rounded to the hundredths place.0.08 to 0.340.16 to 0.240.24 to 0.340.08 to 0.16
Solution
To calculate the 95% confidence interval for this population proportion, we first need to find the sample proportion (p̂) and the standard error (SE).
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Calculate the sample proportion (p̂): This is the number of "successes" (people considered affluent) divided by the total number of people surveyed. In this case, p̂ = 32/267 = 0.11985.
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Calculate the standard error (SE): The formula for the standard error of a proportion is sqrt[(p̂ * (1 - p̂)) / n], where n is the number of people surveyed. In this case, SE = sqrt[(0.11985 * (1 - 0.11985)) / 267] = 0.021.
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Calculate the 95% confidence interval: The formula for a 95% confidence interval is p̂ ± 1.96SE. In this case, the confidence interval is 0.11985 ± 1.960.021 = (0.078, 0.161).
So, the 95% confidence interval for the population proportion is 0.08 to 0.16.
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