Question

The Food Marketing Institute shows that 17% of households spend more than $100 per week on groceries. Assume the population proportion is p = .17 and a simple random sample of 800 households will be selected from the population.

a. Calculate σ(p), the standard error of the proportion of households spending more than $100 per week on groceries (to 4 decimals).

Answer 1

The standard error of the proportion can be calculated using the formula σ(p) = sqrt((p * (1 - p)) / n), where p is the population proportion and n is the sample size. In this case, the standard error is 0.0132.

Step-by-step explanation:

To calculate the standard error of the proportion, we can use the formula σ(p) = sqrt((p * (1 - p)) / n), where p is the population proportion, and n is the sample size.

Given that p = 0.17 and n = 800, we can substitute these values into the formula to find the standard error:

σ(p) = sqrt((0.17 * (1 - 0.17)) / 800) = sqrt(0.13903 / 800) = √0.00017379 = 0.0132

Therefore, the standard error of the proportion of households spending more than $100 per week on groceries is 0.0132 (rounded to 4 decimal places).