A market research company conducted a survey to find the level of affluence in a city. They defined the category "affluence" for males earning $100,000 or more annually and for females earning $80,000 or more annually. Out of 267 persons who replied to their survey, 32 are listed under this category.
The standard error of the sample proportion is __________.
To determine the standard error of the sample proportion, we need to use the formula:
Standard error of the sample proportion (SE) = sqrt(p * (1-p) / n)
Where:
- p is the proportion of individuals in the category of affluence (males earning $100,000+ or females earning $80,000+).
- n is the total number of respondents in the survey.
In this case, the number of respondents in the survey is 267, and the proportion of individuals listed under the affluence category is 32/267.
Let's calculate the standard error:
SE = sqrt((32/267) * (1 - 32/267) / 267)
After doing the calculations, the standard error of the sample proportion is approximately 0.0216 (rounded to four decimal places).
To determine the standard error of the sample proportion, we need to know the sample proportion, which represents the proportion of individuals in the survey who belong to the defined category of affluence.
In this case, we are given that 32 out of 267 persons belong to the defined category. Therefore, the sample proportion can be calculated by dividing the number of individuals in the defined category by the total number of respondents:
Sample Proportion = Number of individuals in defined category / Total number of respondents
Sample Proportion = 32 / 267
To calculate the standard error of the sample proportion, we can use the following formula:
Standard Error = sqrt((Sample Proportion * (1 - Sample Proportion)) / Sample Size)
Sample Size refers to the total number of respondents.
Therefore, the standard error of the sample proportion can be calculated as follows:
Standard Error = sqrt((32/267 * (1 - 32/267)) / 267)
Performing the calculations, we arrive at the standard error of the sample proportion.